Prohibition Of Lead In Children Candies Free Writing Sample

For quite a long time, researchers and wellbeing specialists have followed child lead intoxications from paint, leaded gas, soils, dust, lead-patched jars and water lines, and lead-coated stoneware. Children poisoning with candies containing lead keeps on being a significant general well-being concern. Lead has no organic job in the body and any discernible lead level is strange. Children are likely in danger of unfavorable impacts from lead and cadmium intoxications because of the impacts of these components on creating minds. Youth lead harming is a multi-layered, complex condition, which influences the youngster’s well-being and prosperity, in addition to the family’s lodging security, monetary status, employer stability, and anxiety. Infants and youngsters are at higher danger than older generations for lead openness because of their more modest size and proportionately bigger portion of ingested poisons, their closeness to ground earth and indoor residue, their energy and interest, their oral exploratory and pica practices, their proportionately bigger everyday water and milk admission, and dietary inclinations that vary especially from those of adults (Spungen, 2019). Ongoing lead openness causes depression, cerebral pains, animosity and cognitive decline.

The Industrial Revolution released another influx of lead harming far more prominent than anything in antiquated occasions, and this time it was the common laborers as opposed to wealthier communities who endured the worst part. Derbyshire lead sweets, for instance, were frequently set apart by a dark line across their gums (Maxwell & Neumann, 2008). This was caused by the substance response between lead in the blood and sulfur delivered by microscopic organisms in the mouth, after they had eaten specific sorts of food, including eggs (Maxwell & Neumann, 2008).

Albeit this was an undeniably more weak wellspring of harming than Roman or Victorian paintworks, it was especially more sweeping, influencing each city in the world. Furthermore, this time the casualties were children. It was another American, the pediatric therapist Herbert Needleman, who was liable for at long last getting the lead removed from petroleum (Lynch, 2000). During the 1970s and 1980s, he found that even extremely low degrees of lead openness harmed newborn children, including unborn infants (Lynch, 2000). As they grew up, their intellectual development was slow, they experienced difficulty concentrating, and frequently exited at school. As adolescents, they were bound to become reprobates, unfaithful guardians, drug addicts, and jobless.

Youngsters were first perceived as predisposed to the damaging effects of lead in 1892, however, the negative impacts of lead have been perceived as far back as 600 B.C (Lynch, 2000). Of the 164 California Department of Public Health food defilement cautions given more than 14 years, 42 percent were for lead in sweets (Maxwell & Neumann, 2008). Virtually the entirety of that candy was imported from nations like China, India, and Mexico. Lead harming in children was first archived in Australia in the last piece of the19th century and the early piece of the twentieth century by Dr. J. Lockhart Gibson. Since the mid-1990s, the US FDA, the California Department of Health Services (CA DHS) and free papers, for example, Orange County Register (OCR) in California have announced that specifically imported confections contain lead.

A broad examination of lead in confections started in California by the Orange County Register in October 2002 (Spungen, 2019). While a paper examination does not comprise a logical report, OCR featured the issue of lead-spoiled confections. In the OCR study, an aggregate of 180 trials of confections and coverings were directed on 25 brands at research centers (Spungen, 2019). Eight brands of confections were found to contain risky degrees of lead. Starting on 26 April 2004, the CA DHS likewise discovered raised degrees of lead in 112 unmistakable brands of confections. Of those 84 were made in Mexico, and 8 were made in different nations (Hauptman et al., 2017). FDA has given various direction records, import cautions, and letters to makers on this issue. In December of 2005, FDA gave a draft direction lessening the suggested level of lead in Mexican-style candy from 0.5 ppm to 0.1 ppm or less (Hauptman et al., 2017). FDA additionally included powdered tidbit blend items containing mixes of salt, stew powder, sugar, and flavorings inside the general classification of Mexican treats subject to guidelines in its draft direction (Hauptman et al., 2017). Late examinations have shown that lead openness keeps on representing a well-being hazard in Mexico (Spungen, 2019). Children are a weak populace for lead impacts and Mexican candy has been discovered to be a wellspring of openness in children.

Lead is a harmful hefty metal that is known to cause formative postponements, neurological complications, and other serious medical conditions in individuals, all things considered. It keeps on being among the most well-known and genuine ecological well-being dangers to children younger than six. Most young representatives are harmed through ongoing, low-level intoxications. Subsequently, recognizing and eliminating all sources of lead poisoning in children is a primary concern. FDA’s assessment and testing for lead polluted confections is beyond the extent of this article; notwithstanding, enormous shipments of confections brought into the United States are dependent upon intermittent FDA review.


Hauptman, M., Bruccoleri, R., & Woolf, A. D. (2017). An update on childhood lead poisoning. Clinical Pediatric Emergency Medicine, 18(3), 181–192. Web.

Lynch, R. A. (2000). Lead-contaminated imported tamarind candy and children’s blood lead levels. Public Health Reports, 115(6), 537–543. Web.

Maxwell, E. D., & Neumann, C. M. (2008). Lead-tainted candy: A possible source of lead exposure to children. Toxicological & Environmental Chemistry, 90(2), 301–313. Web.

Spungen, J. H. (2019). Children’s exposures to lead and cadmium: FDA total diet study 2014-16. Food Additives & Contaminants: Part A, 36(6), 893–903. Web.

Use Of Illness Narratives Of Patient/ Client Journey

Preamble and Rationale

The definition of health considers diverse elements and factors. Some of these include the physical, mental as well as the social aspects of individuals (Edlin & Golanty 2010, p. 5). It is obvious that the mere absence of infirmity does not guarantee the proper health of an individual. Breast cancer is one of the prevalent long-term conditions. This complication is predominantly evident in the females. Indeed, it is evident that diverse lifestyle practices may increase or lower the susceptibility of individuals to this condition. There is an eminent significance of the utilization of patient narratives in such contexts.

Narratives might portray the aetiology and prognosis of a particular disease. The analysis of the “health belief model” is vital. Many people may not entirely achieve the state of well-being during all times. Most people present the relativist or maturity perception of personal health. A majority of health professionals uphold the biomedical model as applicable in disease process (Hurwitz, Greenhalgh & Skultans 2004, p. 11). The model potentiates that any health complication is identifiable and may be categorized. In this model, there is recognition of diverse disease classifications. There exists an assumption that bacteria, defective genes, and viruses may be the potential precursors of various health complications.

Other non-physical factors lead to the development of various long-term conditions. The biomedical model also indicates that the identification of various illnesses is a sole preserve for the medical experts (Klugman & Dalinis 2008, p. 16). In this perception, the indulgence of laypersons in the disease identification remains negligible. The recognition of basic disease symptoms is critical. In the process of this identification, there is a correlation of the importance of discourse between the client and the medical expert. The biomedical model emphasizes on the fact that there should be minimal or no discussion between a medical expert and the relevant patient. In this presentation, the biomedical model indicates that this discussion remains fruitless. Consequently, this can never result into an appropriate agreement. However, this conviction remains largely fallacious in some instances.

There is an urgent need to develop an appropriate conversation and narrative between the patient and the doctor. This concept denotes the basic theme in this discussion paper. A bio-psychosocial model presents an alternative explanation on the concept of illness and nurse-patient relation. It indicates that the current health care provision mechanism largely depends on curative. This is relative ton preventive approaches (Charon 2006, p. 22). There is minimal attention for the preventive mechanisms for disease management. These mechanisms might involve behavior change practices. These focus on a progressive transformation of individual lifestyles. Indicatively various approaches are applicable in this process. Some of these might include the application of personal confessions. These are usually attainable with personal narratives. This model emphasizes the significance of lifestyle and its consequent influence on the health of individuals.

It is appropriate to indicate that the bio-psychosocial model presents a more rational way of dealing with health complication. This is evident in the intricate situations in life. However, the reinforcement of the practice of this model with elements of interactions and personal narratives remain critical. Specifically, this relates to the comprehensive management of the particular disease conditions. The bio-psychosocial model criticizes the importance of pure medicine in the minimization of prevalent public health challenges. Analytically, the application of biomedical model excludes the basic social causes related to notable health complications (Taghian & Halyard 2012, p. 18). There is an eminent significance in the development and utilization of information pertinent to any disease condition in humans. The application of narratives is an important strategy in the accomplishment of this objective. Narratives refer to individual presentations on the encounters of diseases and well-being. These presentations occur between the patient and nurse or doctor through stories.

Presently, there is an evident application of these narratives in the practice of psychiatric medicine. Accordingly, it is observably important within other medical fields. From narratives, vital lessons about the patient care are evident. These might concern issues relating to medical ethics, legal issues and the general social concerns on patient health. The fundamental interactions between the patient, nurse as well as other care providers offer critical instincts into the disease prognosis. Presently, there exist eminent intensive research and clinical assessments based on the narrative concept and the practice of medicine (Pathak & Sinha 2008, p. 27). Particularly, these relates to the contribution of individual narratives to the essential developments in the process of medical law or ethics. The medical professionals including nurses might also apply the narrative approach in diverse ways. For instance, it might be applicable in guiding them during their therapeutic practices.

The narrative approach remains widely applicable in the examination and therapeutic management of cancer patients. Breast cancer is one of the long-term illnesses in which the strategy remains appropriate. Individual lifestyles play a momentous role in an individual’s acquisition, development and susceptibility to any infection. Particularly, behavior change remains crucial. Individuals adopt healthy behaviours to be able to live less susceptible lifestyles. There is an increasing emphasis on the utilization of healthy behavior (Taghian & Halyard 2012, p. 31). Principally, this is observable within the present globalized society. Behavior change initiatives help to enhance the general health of individuals. Apart from this, they also strive to prevent people’s susceptibility to infections. These include chronic diseases such as cancer. The concept includes daily life practices. These might encompass activities within the household and in other external environments.

Evidently, there exist dangerous behaviours and lifestyle activities within the general population (Edberg 2010, p. 22). This is because they increase the level of susceptibility of these persons to notorious infections. Health institutions associate specific behaviours to certain diseases and health conditions. This trend is also indicated within different investigations. Some of these include cigarette smoking, drug and substance abuse, lack of appropriate physical exercise and excessive body weight. The dietary practices are important lifestyle events that may determine the occurrence of diseases. There are treatment believes pertinent to the customary and modern societies. These directly dictate individual practices and convictions about healthy behaviours. In addition, they can also influence the therapeutic procedures applicable for specific disease types. The significance of the relationship between narratives and medical practice is unavoidable. Particularly, this relates to nursing practice and care (Charon 2006, p. 32).

Generally, narratives contribute in the creation of awareness about the clinical prognosis and path of a particular infection. Through narratives, nurses are able to obtain the relevant disease history from the patients. The process aids in the elevation of communication and feedback mechanisms among the patients, nurses, caregivers and other important practitioners. The patient‘s historical presentation in the narrative is critical. This is because there is a comprehensive presentation of all issues relating to the development of the disease (Hurwitz, Greenhalgh & Skultans 2004, p. 27). The concept is very important in the rejuvenation of the lives of relevant individuals. Apart from this, there is a possible communication of a positive lifestyle and healthy behavior. The present globalized society has diverse cases or incidences of chronic illnesses. Consequently, there is need to apply more patient narratives concerning these chronic diseases.

Talcott Parsons demonstrated the significance of “the sick role” in patient-doctor relationship and in the healing process (Edberg 2010, p. 31). According to the structural functionalist, the operations of notable social practices remain vital. The role of every sick individual is critical within the social system. Therefore, the “sick-role behavior” may define the rational extension of sickness behavior. The processes enhance a patient’s capacity to comply with and adopt the required behavior during the treatment procedures. The exclusion of sick people from conducting particular chores or duties is vital. Individuals within the “sick-role” lack an explicit obligation for their predicament. Because they face persistent pressure to get well, the stage appears abnormal and deviant. Those undertaking this role must to cooperate with the appropriate medical care providers. Unlike the biomedical model, the “sick-role” indicates the social significance of the medical caregivers.

The Narrative

At the age of 54, Mrs. Tonner tells her breast cancer narrative. The female elementary school teacher was also a Christian. Her ethnic orientation was African-American. Presently, she lived a better part of her life in the UK. However, Mrs. Tonner indicated that she spent most of her earlier lifetime in the United States. This included her earlier primary and secondary schooling. It also entailed her university and a huge part of the professional life as an elementary school instructor. It is evident that Mrs. Tonner led the typical middle class level of life while in the U.S. Having an engineer as a husband, Mrs. Tonner was able to afford basic amenities. These also included some leisure activities and secondary needs. She grew in a culture predominated with western practices and civilization.

Indicatively, these played a remarkable role in the dictation of her dietary practices. Apart from this, the culture had significant influence on her health-seeking pattern and the general behavior. The middle social class has a typical way of life. This is observable within most of the westernized nations globally. In this perspective, it is critical to note that Mrs. Tonner faced the challenges and benefits associated with the middle class. Her religious life was purely Christian. This means that she practiced the fundamental believes of the Christian society. Despite several campaigns and predominant communication on the media about breast cancer, Mrs. Tonner never took heed. In her imaginations, breast cancer was a unique health complication that rarely occurred within populations (Edberg 2010, p. 52).

Personally, she attributed the condition to negative and deviant lifestyles and practices. She indicated that she never had any potential worries on the issue of breast cancer. This was notable from the time of her early childhood through the puberty and adolescent age. As a young youth, Mrs. Tonner provided less attention to basic health messages. These were predominant in the media and college environment. Indeed, she refuted these health communication messages up to her later lives in marriage. Partly, she admits that during these periods, these health messages were never comprehensive. They never included pertinent information regarding the breast cancer disease, its diagnosis, and consequent treatment and management (Charon 2006, p. 68). However, the turning point was during the launch of a major breast cancer campaign. The campaign occurred within the elementary school in which Mrs. Tonner was an instructor. Through this campaign, Mrs. Tonner was able to gain critical information on the issue of breast cancer.

It was unknown to her that at the age of fifty-two and when almost retiring, she started developing breast cancer. Later, she sought to attend medical diagnostic procedures from a qualified medical practitioner. She denoted that relatively low level of health assistance for the female patients within the public health care facilities. Particularly, she indicated that the trend was worse for the American-Whites. The breast cancer enabled Mrs. Tonner to conduct a personal breast examination. This formed the basis of the reason for seeking expert medical advice. With limited knowledge on the issue of breast cancer, Mrs. Tonner underwent immense mental torture. To her, the family was an important unit. She feared that her family could be impaired by the incidence (Edberg 2010, p. 81).

She also developed a considerable level of depression and anxiety. This was because of her negative anticipations as a future cancer patient. The limitations and lack of proper information on breast cancer within the public health facilities she attended had severe consequences. One of these included the notable delay in her knowledge about whether she had the disease or not. For a remarkable period, Mrs. Tonner had to visit many different health care institutions to seek for the appropriate information. It was after some six months that she sought for the services of a cancer expert. This was a private consultant. Many investigations indicate the role of complementary and alternative therapy for chronic conditions amongst diverse populations. Others also emphasize on the importance of seeking expert knowledge and services for chronic conditions such as breast cancer (Taghian & Halyard 2012, p. 41).

The tormenting period and uncertainty pushed Mrs. Tonner to seek for an expert advice on the breast cancer situation. Breast cancer has severe implications on the affected persons. A part from destruction of an individual’s beautiful look, the person also suffers huge loss of food nutrients in the entire body. The development of metastatic cancer is, particularly, dangerous for most body cells. These carcinogenic forms are likely to spread to other potential sites within the body (Charon 2006, p. 72). Therefore, a cancerous anatomical location of the body must undergo total elimination. The private consultant offered to Mrs. Tonner more advanced and precise diagnostic processes. These involved an initial orientation into the possible causes of cancer. Apart from this, she underwent basic orientation on the types of cancer, their critical stages and the ultimate management procedures.

The consultant applied the mammogram in the initial identification processes. However, as a confirmatory test, the next diagnostic procedure entailed the use of the contemporary ultrasound (Hurwitz, Greenhalgh & Skultans 2004, p. 81). These had adequate competency in the provision of reliable diagnostic information about the state of cancer. Most cancer experts reiterate on the detrimental impacts of cancerous anatomical body parts. In such contexts, they provide amputation as the basic method for preventing further or extensive spread of the cancer to other body parts. The consequent diagnostics after the ultrasound involved the use of tissue biopsy. This refers to a simple surgical process in which there is tissue siphoning and application of microscopic techniques. The basic aim of the procedure was to assess the presence of timorous cells.

The confirmation tests revealed that Mrs. Tonner suffered from severe Invasive ductal carcinoma (IDC). This breast cancer is very popular (Taghian & Halyard 2012, p. 45). Further revelations indicated that the cancer managed to invade various tissues within her breasts. The condition remained incurable. Therefore, the private consultant indicated management as the most preferable and rational option. This meant Mrs. Tonner had to seek transformative health care option. To make it worse is that the revelation emerged at a time when she was on the verge of relocating to the UK for a two-year long holiday. This was important in many ways. For instance, it meant that she could not enjoy the care provision from most of her family members. A series of consultations carried out by the private consultant enabled him to draw an appropriate cancer schedule.

Mrs. Tonner was inducted on other basic forms of breast cancer. Some of the highlighted forms included the “recurrent and metastatic cancer.” Other highlighted forms were the “ductal carcinoma in situ” (DCIS), “invasive lobular carcinoma” (ILC) and the “cribriform carcinoma of the breast” (IDC) among other forms (Kasper & Ferguson 2002, p. 67). After a thorough coaching on all these cancer forms and their pathogenesis, the cancer expert resorted to psychosocial support strategies. This involved an induction on the negative causes of the particular breast cancer. These included the use of hormonal contraceptives. It is critical to note the various ethical concerns pertinent to the management of cancers. The recognition of confidentiality remains important (Pathak & Sinha 2008, p. 77). This explains why this narrative uses a hypothetical name. This helps to hide the overall identity of the real breast cancer patient. Furthermore, it is important to indicate that the full informed consent of the patient was necessary prior to the beginning of the narrative.

Notably loopholes are evident in the process of this diagnosis. For instance, there is lack of adequate information on all the forms of breast cancer. Additionally, the patient was not part of the decision processes and consultations made by the doctor. Observably, these undertakings are largely against the ethical and professional conduct provisions stipulated by the national health policies on cancer management. During the clinical management processes, Mrs. Tonner also sought for other complementing interventions. The spiritual counselling processes had significant implications to the patient. The clinical management process took place in a consecutive manner. The patient underwent the processes of chemotherapy ((Edlin & Golanty 2010, p. 89). Moreover, the cancer specialist also advised the patient to undertake the radiography processes. These were very critical steps in the life of the patient. However, following the one year of undergoing all these processes, it was sad that Mrs. Tonner suffered a serious hearing and weight loss.

She needed comprehensive care from her children. Generally, there is diverse lifestyle factors associated with different disease conditions. Other than these individual factors, the external factors including socioeconomic issues have potential health impacts. Poverty might also lead to the development of certain health conditions. Since Mrs. Tonner came from a middle class, it is notable that poverty had minimal influence in the development of the disease condition. The importance of nutritional counselling is eminent in this scenario (Rice 2000, p. 107). After a long duration of nutritional counselling and assessment, it was notable that the patient developed the breast cancer out of her dietary practices. However, it is important to recognize that unlike the poor persons, she was able to access quality medical attention.

Patient monitoring and close observation is critical during any therapeutic processes (Lundy & Janes 2009, p. 111). There are several cases where patients fail to adhere to their prescriptions. On the case of Mrs. Tonner, many factors led to the development of non-compliance to various drug therapies. Foremost, the use of other complementary and alternative healing methods was an important factor. Lack of close observation and monitoring by the private medical consultant was another contributory factor. There are extensive investigations on the issue of various sociological, cultural and individual influences on the health of personalities.

The experiences of Mrs. Tonner were very important. She stressed on the need for people to transform their health seeking behavior. She also advocated for impartiality in the quality of health service provision. Moreover, Mrs. Tonner advised everyone to adopt healthy dietary practices. She indicated the importance of engaging in discussions (Edberg 2010, p. 122). Specifically, this concerns the people suffering from long term conditions. There are loopholes in the management of long-term conditions. Evidently, this necessitates the need to launch more strategic and empirical investigations. This is vital in the reduction and management of the high incidences of breast cancer.


Charon, R 2006, Narrative medicine: honoring the stories of illness, Oxford University Press, Oxford.

Edberg, C 2010, Essential readings in health behavior: theory and practice, Jones and Bartlett Publishers, Sudbury, MA.

Edlin, G & Golanty, E 2010, Health & wellness, Jones and Bartlett Publishers, Sudbury, MA.

Hurwitz, B Greenhalgh, T & Skultans, V 2004, Narrative research in health and illness, BMJ Books, Malden, MA.

Kasper, S & Ferguson, J 2002, Breast cancer: society shapes an epidemic, Palgrave, New York, NY.

Klugman, M & Dalinis, M 2008, Ethical issues in rural health care, Johns Hopkins University Press, Baltimore.

Lundy, S & Janes, S 2009, Community health nursing: caring for the public’s health, Jones and Bartlett Publishers, Sudbury, MA.

Pathak, K & Sinha, K 2008, Bio-social issues in health, Northern Book Centre, New Delhi.

Rice, H 2000, Handbook of stress, coping, and health: implications for nursing research, theory, and practice, Sage Publ, Thousand Oaks, CA.

Taghian, G & Halyard, Y 2012, Breast cancer, Demos Medical Pub, New York, NY.

Mathematics: The Movement Of An Engine Piston


Many people sit comfortably inside a car and enjoy this amazing technology without understanding the driving force behind the motion of a car. Moreover, others may have opened the hood of a car and wondered how this confusing jumble-like metallic structure called the engine, fitted with a mesh of wires and tubes executes its motion. In the face of all these dilemmas, the terminologies synonymous with the gurus of this awesome technology, for instance, the 3.0-liter V-6 engine leaves many others confused. Given all confusion, the literature in this paper will focus on the basic principle behind the engine, the pieces that constitute the entire staff, and finally, conclude on the research question- how we can improve the speed of a car with regards to piston modifications.

To increase the efficiency of a car’s engine, various elements require modifications. Among the elements that require alterations include the cylinder head and the rpm (revolutions per minute) of the crankshaft. As regards the modifications done on the cylinder head, terminology such as the ‘stroke,’ which is the diameter of the bore through which the piston travels, is widely used. This is the parameter that is adjusted.

On the other hand, when the focus is on the rpm of the crankshaft, such terminologies as the rod length and the torque are commonly used, and hence; require modifications. Importantly, since the rod and the crankshaft work in tandem and depend on the speed of the piston, a factor influenced by the stroke, it is important to optimize on all these factors to achieve maximum performance. The principle behind an engine motion

Whatever transpires in the inside of the engine to spark motion is energy transformation. Ideally, in the engine, the energy is transformed from chemical energy (gasoline/petrol chemical reaction) into mechanical energy via engine piston/crankshaft assembly. It is the motion of the pistons and the crankshaft that sparks the motion of a car. The common mechanism employed by the current engine designs is that they burn the fuel in-situ, eventuating in a motion. As such, these types of engines are christened internal combustion (IC) engines. Figure (1) below portrays the image of an IC engine, giving the details of its parts.

The cross-section of the IC engine, portraying its basic parts
Figure 1 : showing the cross-section of the IC engine, portraying its basic parts (Horst 72).

Before getting further, there are two things we need to note. First, there exist a variety of these types of IC engines based on the fuel used: these include the diesel engines and gasoline engines (Anyebe29); other variations of the IC engine e.g. rotary and HEMI engines exist, exhibiting their own merits and demerits. Second, as opposed to the internal combustion engine, there is also the so-called external combustion engine. To this end, an ancient technology, the steam engine, is an example of this type of engine. For this type of engine, fuel is burned externally to generate steam, which later sparks motion inside the engine. Of the two, the former is more efficient and significantly smaller than the latter (Horst 73).

Internal Combustion

The principle here is that the reciprocating combustion happening within an engine is continuously converted into mechanical motion. For instance, an air-gasoline mixture placed inside an enclosed container, called the cylinder (a, b), is ignited (c); a huge bang is heard releasing an awesome amount of energy due to the air-gasoline mixture expansion as gas.

How combustion inside the cylinder happens in that order (a), (b), (c) and (d) to execute motion
Figure 2: Showing how combustion inside the cylinder happens in that order (a), (b), (c) and (d) to execute motion (Horst 73).

This gas expansion pushes against a moving piston connected to the crankshaft assembly, thus causing the rotation of the crankshaft. As the crankshaft rotates, the piston is pushed back into the cylinder. As the piston is pushed back, a valve opens to release gas trapped inside the cylinder cavity (d). Once the piston completes a complete cycle, another valve opens for the air-gasoline mixture to flow in.

The piston goes through another cycle of expansion, thus pulling more air-gasoline mixture into the cylinder cavity then compressing, thus compressing the air-gasoline mixture, before it is ignited again. This is known as a four-stroke combustion engine. Contemporary engines are typically four-stroke combustion engines. This engine, also known as the “Otto cycle” is the brainchild of Nikolaus Otto, an invention he made in 1867” (Horst 73). The details of the engine combustion chamber are exhibited in the picture below:

The four strokes of an engine’s piston. 1 shows the intake stroke, 2 is the compression stroke, 3 is the combustion stroke, and 4 is the exhaust stroke
Figure 3: showing the four strokes of an engine’s piston. 1 shows the intake stroke, 2 is the compression stroke, 3 is the combustion stroke, and 4 is the exhaust stroke (Doutor 65)

The mathematics behind the piston motion

The linear motion of the piston within its housing or cylinder cavity is quite simple. Though simple, the motion within the cylinder requires high design precision and follows precise mathematics. Consider the cross-section illustration of a typical piston as shown below.

The geometrical approach of the engine’s piston.
Figure 4: showing the geometrical approach of the engine’s piston (Gunston 67).

The table below shows the identities of all the unknown parameters shown in the figure above.

Acronym/symbol Definition
TDC Top dead-end center
BDC Bottom dead-end center
CID Cubic inch displacement
TQ Torque
B Bore
L Length of the connecting rod
S Stroke length
H Piston height relative to BDC
a Crankshaft radius
θ Crankshaft angle

Table 1: shows the identities of all the unknown parameters on the figure.

To calculate the piston height (position), consider the figure below:

The geometrical derivation of the components of the engine’s piston.
Figure 5: showing the geometrical derivation of the components of the engine’s piston (Gunston 67).

Given the crankshaft angle θ and the crankshaft radius (a), the additional components, aCos(θ)  and aSin(θ), we can define piston height using Pythagoras theorem, as follows:


When the connecting rod is at the BDC position, i.e., the crankshaft radius points downwards, (θ=180°), h = L-a; and at TDC (θ = 0°), h = L+a. When the piston height is plotted vis-à-vis θ as per a revolution, the below wave is obtained.

The crankshaft motion in relation to the instantaneous height of the piston.
Figure 6: showing the crankshaft motion in relation to the instantaneous height of the piston.

A θ=0.2П , the piston is at TDC, therefore, h is maximum +a. The reverse is true when the piston is at BDC when θ=n (Gunston 67).

As anticipated, the piston height is highest when the crank angle equals 0 and 2 π (Setright 44).

Also, the volume of the piston cavity (cylinder) can be calculated.The maximum volume coincides with the piston position at the BDC. As such, this volume is given by:


Instantaneous volume can be obtained as below:


Where; H represents the height of the piston about the BDC. When we substitute the term S with the derived terms above we obtain:


Astheg that we adimensionsg with a piton ithte following dimnsions; Formula A the plot of the volume versus the crank angle, as expected, reveals the pattern below with the maximum volume coinciding with the π (3.142).

The relationship between the piston volume and the crankshaft angle
Figure 7: showing the relationship between the piston volume and the crankshaft angle (Gunston 67)

Similarly, the surface area of the piston is given by the sum of the inner areas of the cylinder head and that of the inner curved surface. Therefore, this is given by:


On substituting the values of S and H we obtain:


Consequently, with the above formula, one can evaluate how the piston height responds to the changing angular velocity of the crankshaft. This can then be plotted for analysis.

In this respect, if we assume that a car’s crankshaft with a= 0.5m and L= 1.5m was initially moving at a speed of 105 rads/s for one second, and then started to accelerate steadily to a speed of 210 rads/s within a second and remained constant, the below plot (figure 8) would be expected.

From the above information we derive the formula for finding the angular velocity as below: ω=Δθ Δt

Integrating the function between 1 and 2 seconds:


When θ =105 or 210 rads/s the angular positions are given as below:


Therefore, to find the trend of piston height (h) during the course of motion we apply equation (1) as below:


From the above equations you can find the different values for h between 1 and 2 seconds but in regards to their respective conditions to obtain the trend below.

The plot of instantaneous piston height for a car accelerating from a crankshaft speed of105 rads/s to 210 rads/sec within a second.
Figure 8: showing the plot of instantaneous piston height for a car accelerating from a crankshaft speed of105 rads/s to 210 rads/sec within a second (Gunston 67).

Firing order

So far we have discussed the four-stroke cycles a single-piston goes through to turn a crankshaft. While a single piston can produce rotational power, it is not sufficient however for the practical locomotive. Further, from a mechanical point of view, a single-piston motor does not constitute an efficient or workable engine design. Accordingly, typical engines are produced with multiple pistons arranged in such a way as to work cooperatively to produce enough power as well as synchronized continuous motion. Typically, engines are designed with even number piston-arrangement, though there exist engines with an odd number of pistons.

As stated earlier, the internal combustion of the compressed fuel inside the cylinder is what derives the entire motion of a piston. So, for engines with multiple piston-arrangements, the internal combustion (sparkplug ignition) must occur in a synchronized fashion for the engine to produce practical and efficient motion. Now the question that lingers in the mind of many is how sparkplug synchronizes its sparking order concerning the appropriate position of each piston? The green light to spark or ignite the sparkplug is what is termed as the ‘firing order.’ Ideally, this firing order is synchronized in such a way that it is ignited when each piston is in the fuel compression stage.

The sparkplug firing order is normally regulated by the distributor which sends currents accurately in pulses concerning the position of the piston during the entire cycle. The opening and closing of the valves that control the fuel flow inside the cylinder and exhaust are also synchronized and controlled by the mechanical assembly known as the camshaft. The piston movement also drives the camshafts and they are programmed to open and close the valves in a specific sequence to optimize the internal combustion and exhaust process as well as minimize undesirable effects e.g. uncontrolled vibration. For instance, in an in-line engine the plugs are named according to their positions concerning the engine from the anterior to the posterior in that order i.e. 1, 2, 3, and 4 (see figure 9 below).

Engine pistons, numbered to elaborate how the firing order is executed to avoid undesirable effects e.g. extreme vibrations. The firing order is alternate to mitigate vibration effect.
Figure 9: engine pistons, numbered to elaborate how the firing order is executed to avoid undesirable effects e.g. extreme vibrations. The firing order is alternate to mitigate vibration effect.

Engine optimum power output is produced normally when pistons are fired in sequence. So, during the compression stroke of each piston, a spark is emitted just before “the piston reaches top dead center (TDC) on the compression stroke” (Singal 38). However, assuming the compression stage in each piston is arranged to occur in sequence, i.e., 1, 2, 3, and then 4, the sparkplugs will also be arranged to fire in the same order. In such a case, the undesirable effect of enormous vibration would be felt thanks to the impulses emanating from the four pistons as they fire in one direction, i.e., 1, 2, 3, and then 4.

To decimate this effect, the compression stage and the sparkplug firing are arranged alternately e.g. 1, 3, 4, and 2. In this regard, mechanics ought to take caution when replacing the high-tension leads connecting the sparkplugs since a blunder in their placement may interfere with the correct sequence of the firing order, which may lead to undesirable effects. To further reduce undesirable effects of vibration and crankshaft hesitation, inertia generated from the rotating crankshaft-attached flywheel is used. Additional weights are further added to the crankshaft to enhance the engine’s stability.

How the valves open and close

The valves attached to the combustion chamber of each cylinder of the engine are named literally as per their functions. As such, we have the inlet valve which acts as a vent through which fuel and air enter the engine, and an exhaust valve, which allows for the expulsion of exhaust fuel. They are synchronized to open precisely and periodically to enhance the smooth running of the engine. This opening and closing mechanism of the valves are controlled by a system that is composed of a pear-shaped lobe otherwise called cams that are mounted on a rotary shaft” (Setright 44). This assembly is referred to as a camshaft. The movement of the camshaft is controlled through a system of gears linking it to the crankshaft (see figure 10 below).

Where the camshaft “is mounted in the engine block, small metal cylinders tappets sit in channels above each cam, and from the tappets, metal pushrod extends up into the cylinder head” (Setright 45). The pushrods incorporate the rocker arm which constantly shuts the valve.

The mechanism of opening and closing is mechanical. First, the pushrod rises to rest on the cam, acting as a fulcrum for the rocker arm. In effect, the rocker arm pushes the valve held by a spring to open. As the camshaft makes a 360o turn, the spring overcomes the rocker arm to close the valve. This mechanism is dubbed the overhead-valve (OHV) system. Some designs don’t have pushrods thus they achieve this function courtesy of camshafts located in the head cylinder overhead-cam (OHC) system.

The overhead valve (OHV) (1) and the overhead-cam (OHC) (2) systems vital in opening the engine valves to allow air to enter the engine. It also allows exhaust air to exit the engine.
Figure 10: showing the overhead valve (OHV) (1) and the overhead-cam (OHC) (2) systems vital in opening the engine valves to allow air to enter the engine. It also allows exhaust air to exit the engine (Singal 38).

The basic engine parts/layout

The engine is the ‘heartbeat’ of the car, and it is the linear motion of the piston that eventuates in the motion of the car. The battery of reactions that results in this motion is executed by the sparkplug, which emits sparks, a source of heat that burns air-fuel mixture in-situ in what is dubbed internal combustion. To endure the massive workload, the engine ought to portray robustness in its structure. To this end, the engine is a composite of two basic structures: the massive lower structure housing the pistons (the cylinder block), and a lighter upper structure enclosing the head cylinder. The cylinder head is where the vents for air and fuel are located, and in isolated designs, this part also has vents designed to expel the exhaust fuel-air mixture.

The block is composed of the crankshaft, a structure that transforms the reciprocating “linear motion of the pistons into rotary motion of the crankshaft” (Horst, 1999). Moreover, the cylinder block encases the camshaft, a structure responsible for the periodic opening and shutting of the valves. The cylinders of the piston system “are cast into the block, as are mountings for ancillary equipment such as a filter for the oil which lubricates the engine, and a pump for the fuel” (Gunston 48). At the periphery of the crank casing at the bottom of the cylinder block is the slump, an oil reservoir (figure 11). The material choice for these basic parts depends on the density and the ease to dissipate heat. To this end, aluminum is the most preferred material since its light and has good conductivity.

Having looked at the engine’s basic parts, it is important to understand the engine layout. Engine designs come in three different styles; the vertical layout, the V-shaped, and the horizontal shape. The vertical layout is the most popular design, with all the pistons aligned in a vertical position and the same direction (see figure 11 below (1). On the other hand, while the V-shaped design (2) limits the angle between successive cylinders to within reflex angles, a horizontal layout (3) has this angle permanently at 1800 (Vegburner 20).

The different engine layouts: 1 is the vertical layout, 2 is the triangular layout and 3 is the horizontal layout.
Figure 11: showing the different engine layouts: 1 is the vertical layout, 2 is the triangular layout and 3 is the horizontal layout (Singal 38).

How the piston of the engine of a car can be modified to improve a car’s speed

An engine’s efficiency can be modified on various fronts to optimize its performance. The areas that need optimization include among others the cylinder head, the general efficiency of the engine, and the rpm of the crankshaft. Of note, one common thing about these parameters is that they are based on geometric relationships. The rpm of the crankshaft is dependent on the piston’s speed, a factor vital in the determination of the overall speed of the car. This part forms the core of our discussion.

The piston’s speed is dependent on the cylinder geometry, which can be optimized by considering the stroke-to-bore ratio. Ideally, the size of the stroke is proportional to both the cubic inch displacement (CID) and the Torque (TQ). This can be explained by the equation below:

Assuming the term h to be the vertical height above the crankshaft, the velocity of the piston head (see figure 12 below) with regards to the crank angle (θ) can be obtained from the derivative of equation (1) – the piston height concerning the crankshaft angle.


On simplifying the expression above we get:



Equation (4) represents the piston velocity.

When we assume that we are working with a piston with the dimensions shown in the figure below (figure 12) we obtain the piston velocity as shown below:

Converting the units to SI units: 39,3701 inches

Therefore; a = 1.973in = 0.0501m

L = 6.1in = 0.1549m

Formula = 0.085 cm/s.

For this piston, the stroke-to-bore ratio is given by L/a is = 3.1

The piston geometry as used to determine the piston velocity.
Figure 12: showing the piston geometry as used to determine the piston velocity (Singal 38).

Now consider a piston with a stroke-to-bore ratio of 4. For this case, let’s assume that the rod length L is the same as the previous piston (0.1549m) and a is equivalent to 0.039m. The piston velocity will be given by:

Formula = 0.064 cm/s

From these results, it is evident that the piston velocity decreases with the increase in the stroke-to-bore ratio. In a synopsis, the efficiency of the engine can be improved by reducing this ratio. CID increases with an increase in piston length L. However, it should be noted that this modification on the flip side increases the friction, which decreases the engine’s horsepower (HP). To reduce friction, rings with low drag coupled with rods made up of lighter materials are applied. In addition, enhanced stroke decreases the rpm. Of note, enhanced torque coupled with minimum rpm translates to swift acceleration. The following examples demonstrate some of the extreme cases that have been experimented with and computed before:

The bore of 12.7 cm with a stroke of 6.1 cm translates to a torque of 421TQ/66.67 Hz, which is equivalent to 380HP/86.67 Hz rpm.

The bore of 10.2 cm with a stroke of 9.5 cm inch translates to a torque of 417TQ/61.67 Hz, which is equivalent to 368HP/83.3 Hz.

A bore of 7.6 cm with a stroke of 17.2 cm translates to a torque of 387TQ/66.67 Hz, which is equivalent to 313HP/78.3 Hz.

From the above analysis, it is evident that the engine’s CID is proportional to the torque. Nevertheless, this effect translates to a decrease in the engine’s horsepower. This happens irrespective of the stroke’s length or the cylinder radius. However, increasing “the bore diameter produces more torque; less horsepower loses to friction than stroking” (Gunston 67). As such, it is recommended to increase the diameter of the cylinder to enhance power, an effect that is enhanced further with more stroking.

Let us now check how the rod-stroke ratio affects the piston’s velocity. Velocity is a real-time rate of change in displacement. Concerning piston, this measurement always tries to establish how fast a piston “changes position concerning the reference point” (Gunston 67). Mathematically, this analysis is referred to as the first derivative concerning the position curve. For the sake of this analysis, the crank rotation is chosen as the reference point.

As it has been mentioned before, the main focus of this analysis is to check on the piston’s position concerning time, an effect that would influence the crank speed. Consider figure (13) below. The piston shifts from TDC to BDC, and therefore, the velocity moves from zero at TDC to an optimum then back to zero at BDC. The magnitude of the optimum velocity and its position vis-à-vis crank position is a function of the R/S ratio.

Both the magnitude and the piston’s position with respect to time, an effect that influences the crank speed.
Figure 13: illustrating both the magnitude and the piston’s position with respect to time, an effect that influences the crank speed.

The figure above exhibits the piston’s position when at the optimum velocity before and after TDC. For this piston, the dimensions are given below:

Stroke = 4 in = 10.15 cm;

Rod length = 6.100 in = 15.24 cm.

As such, the rod-stoke ratio is given by:

15.25/10.15 =1.525

At this position, 73.9o from the TDC, the piston covers a distance given by:


As such, it has completed only 43.9% (4.46/10.16 x 100%) of the entire stroke. With these parameters, and considering that the crankshaft moves at a frequency of 66.67 Hz, the optimum piston velocity obtained is 22.3 m/s (refer to formula 4). Nonetheless, for a longer stroke exhibiting the same rod to stroke ratio, the piston’s position at the peak velocity would be similar; however, the optimum velocity would be greater relative to the above. With this information, it is apparent that the rod-to-stroke ratio affects the eventual speed of the car. In this effect, to enhance the speed of the car, then one ought to maximize the ratio.

Another parameter of equal importance is the mean piston speed (MPS). This parameter is vital in the evaluation of engine efficiency. By definition, MPS is the average value of the piston velocity at a specific rpm. This is possible to establish since we know that the piston covers a distance that is approximately double that of the stroke per revolution. Consequently, the below expression is derived:

  • MPS = RPM x 2 x stroke

As such, the MPS of an engine running at 4000 rpm and having a stroke length of 4 inches is given by:

  • = 4000 x 2 x 4 inches per minute
  • = 2667 feet/minute
  • = 13.55 m/s

Given the equation above, it is apparent that the MPS is proportional to the stroke’s length. To this end, to improve the speed of a car to an optimum level then a designer ought to consider increasing this parameter to its peak. This influences the rate at which the crankshaft revolves.

Works Cited

Anyebe, Andrew. Combustion Engine and Operations, Denver: CO Press, 2009.

Audesirk, Thomas. Engine power, San Francisco, CA: Benjamin Cummings, 2008.

Doutor, Silva. The motion of a piston, Cambridge: Cambridge University Press, 2009.

Gunston, Brown. Development of Piston Aero Engines, Ambler, PA: Lippincott Williams& Wilkins, 2004.

Horst, Holweins. The Middle Ages of the Internal Combustion Engine, Society of Automotive Engineers 34.6 (2010).

Setright, Keith. “Some unusual engines.”Journal of mechanical engineers45.5 (2006).

Singal, Ranjay. Internal Combustion Engines, New Delhi: Kataria Press, 2004.

Singer, Joude. A History of Technology: The Internal Combustion Engine, Boston: Havard Engineering School Press, 1999.

Suzuki, Takuziki. “The Romance of Engines.”Society of Automatic Engineers 56.2 (2003).

Vegburner, Downing. Combustion Chamber Design, New York, NY: New York University Press, 2009.

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