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Physics by Trevor Lipscombe

Journal of Biosciences and Medicines, 2024

Background: Elastomeric pumps (elastic balls into which analgesics or antibiotics can be inserte... more Background: Elastomeric pumps (elastic balls into which analgesics or antibiotics can be inserted) push medicines through a catheter to a nerve or blood vessel. Since elastomeric pumps are small and need no power source, they fit easily into a pocket during infusion, allowing patient mobility. Elastomeric pumps are widely used and widely studied experimentally, but they have well-known problems, such as maintaining reliable flow rates and avoiding toxicity or other peak-and-trough effects. Objectives: Our research objective is to develop a realistic theoretical model of an elastomeric pump, analyze its flow rates, determine its toxicity conditions, and otherwise improve its operation. We believe this is the first such theoretical model of an elastomeric pump consisting of an elastic, medicine-filled ball attached to a horizontal catheter. Method: Our method is to model the system as a quasi-Poiseuille flow driven by the pressure drop generated by the elastic sphere. We construct an engineering model of the pressure exerted by an elastic sphere and match it to a solution of the one-dimensional radial Navier-Stokes equation that describes flow through a horizontal, cylindrical tube. Results: Our results are that the model accurately reproduces flow rates obtained in clinical studies. We also discover that the flow rate has an unavoidable maximum, which we call the “toxicity bump”, when the radius of the sphere approaches its terminal, unstretched value—an effect that has been observed experimentally. Conclusions: We conclude that by choosing the properties of an elastomeric pump, the toxicity bump can be restricted to less than 10% of the earlier, relatively constant flow rate. Our model also produces a relation between the length of time that the analgesic fluid infuses and the physical properties of the fluid, of the elastomeric sphere and the tube, and of the blood vessel into which the analgesic infuses. From these, we conclude that elastomeric pumps can be designed, using our simple model, to control infusion times while avoiding toxicity effects.

American Journal of Physics, 2024

We describe the physics of the “Windkessel effect” and its role in smoothing the output of water ... more We describe the physics of the “Windkessel effect” and its role in smoothing the output of water produced by piston-driven pumps found in early fire engines and modern residential well houses. We also construct a simple, analytical model of its operation and apply this model to the Windkessel in Richard Newsham's 1725 fire engine. We find that Newsham's Windkessel reduces the variations in the pump output stream from a high of 80% to a low of 16%.

European Journal of Physics

Damping of an oscillator is often analyzed in terms of linear or quadratic drag as the object mov... more Damping of an oscillator is often analyzed in terms of linear or quadratic drag as the object moves through a fluid such as air. Here attention is instead focused on the frictional torque in the bearing of a rigidly swinging pendulum. Two simple models are proposed to describe the bearing. First, it is considered to be two concentric cylinders with friction acting at one point of contact between them. Second, the bearing is taken to be composed of small balls in the race between the two cylinders, so that there are many points of contact over which the frictional force is distributed. The level of analysis in these two models is accessible to students in a first university course in calculus-based mechanics.

Latin-American Journal of Physics Education, 2022

A soccer ball is conceptually split into halves so that it can be modeled as two identical blocks... more A soccer ball is conceptually split into halves so that it can be modeled as two identical blocks connected by a spring. A constant kicking force applied to one block simultaneously compresses the spring and imparts velocity to the center of mass of the system. If the half in contact with the foot detaches from it when it reaches a specified speed, the final centerof-mass velocity depends on the spring constant. That could explain why it is hard to kick a soccer ball as far on a cold day (when the spring is stiffer) as on a warm day.

Physics Education, 2021

Physics Education PAPER Cockney acoustics: from how far away can you hear the sound of Bow bells?... more Physics Education
PAPER
Cockney acoustics: from how far away can you hear the sound of Bow bells?
T C Lipscombe3,1 and Ian M Robinson2

Published 5 October 2021 • ©2021 IOP Publishing Ltd
Physics Education, Volume 56, Number 6
Citation T C Lipscombe and Ian M Robinson 2021 Phys. Educ. 56 065028
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Abstract
The most important question for anyone born in London is 'Are you a Cockney?' Only those born within the sound of Bow bells can truthfully answer the question with a resounding 'yes.' 'Cockney' is a term of pride in the heart of the East End, an area recently made internationally famous to a new audience due to the global success of the TV series 'Call the Midwife,' set in Poplar. Here we use simple physics to determine the greatest distance that you can be born and still hear the peal of the bells. As such, it should appeal to all those teaching the physics of waves, or sound, in the Greater London area—and beyond.

The Physics Educator, 2019

A two-equation model is developed to describe the descent of a submarine as it floods its ballast... more A two-equation model is developed to describe the descent of a submarine as it floods its ballast tanks. The flow into the tanks is assumed to be inviscid, and the drag on the vertical sinking motion of the craft is neglected. The two coupled differential equations are the generalized form of Newton’s second law and the Bernoulli relation. Time derivatives are converted to spatial derivatives to decouple the equations, and the resulting second-order equation is solved using the Euler–Cromer algorithm. The theory and the method of numerical integration are suitable for an intermediate-level undergraduate course in mechanics that includes some basic fluid dynamics.

American Journal of Physics, 2021

Two identical objects are simultaneously projected vertically upward with the same initial speed ... more Two identical objects are simultaneously projected vertically upward with the same initial speed in a uniform gravitational field and then return to their starting point. One object is subject to a resistive force proportional to the nth power of its speed where n ! 0, such as linear (Stokes) drag for n ¼ 1 or quadratic (Newtonian) drag for n ¼ 2. The other object moves through vacuum with no resistance. Which object returns to its starting point first? It is shown analytically that the object subject to drag always wins the race if n ! 1, but that either object can win otherwise, depending on the ratio of the launch speed to the terminal speed of the object subject to drag if 0 < n < 1 or depending on the ratio of the frictional acceleration to the gravitational acceleration if n ¼ 0. These analytical results are confirmed by Euler-Cromer numerical integration of the equations of motion.

American Journal of Physics, 2021

Experience teaches us that a large balloon takes longer to deflate than a small one of the same k... more Experience teaches us that a large balloon takes longer to deflate than a small one of the same kind. But what is the quantitative relation between the deflation time τ and the radius R of a balloon? A simple analysis, depending only upon elementary physics, shows that τ∼R7/2—a prediction that is surprisingly easy to illustrate with a party balloon, a tape measure, and a smart-phone app.

Journal of the Washington Academy of Sciences, 2020

In American football, kickers attempt to maximize both the distance travelled by the ball and the... more In American football, kickers attempt to maximize both the distance travelled by the ball and the hang time. These two objectives, though, are mutually exclusive, and result in the kicker’s conundrum or the punter’s paradox: what should the kicker aim for? By means of a simple football observation, we develop a simple expression for the optimal kick in football. In real life, though, the ideal punt is not likely to happen. Kicking camps, which young college prospects attend to catch the attention of coaches, rate kickoffs and punts in terms of a points system based on a simple formula. This we show leads to a different criterion, which rewards “Bigfoot” – the player who can kicker the hardest – over the perfect punter. Young kickers attending the camp should adopt a different strategy, kick according to the equation, and kick as hard as possible. We propose an alternative formula, one that rewards range and hang time, but which punishes violations of the “perfect punt” condition. College coaches on the lookout for kicking and punting talent might want to think again about the rankings generated by such kicking camps.

The Physics Teacher, 2020

Breathing is something we all do, usually without thinking about it. But when viewed through the ... more Breathing is something we all do, usually without thinking about it. But when viewed through the lens of physics, respiration becomes an example of elementary thermodynamics. As shown here, the lungs can be modeled as a two-stroke heat engine. Breathing thereby provides a novel physics application for life science students, demonstrating the basics of the first law of thermodynamics, coefficient of performance, and hysteresis.

European Journal of Physics, 2018

The scattering angles and speeds resulting from an off-centre elastic collision of a smooth puck ... more The scattering angles and speeds resulting from an off-centre elastic collision of a smooth puck or sphere incident on a second one at rest on a frictionless surface are analysed in terms of the impact parameter and mass ratio. Particular attention is paid to finding simple special cases for the final angles or the relations between them that could be explored in homework problems or laboratory experiments. The level of analysis is accessible to an introductory undergraduate physics course.

European Journal of Physics, 2018

The brachistochrone problem consists of finding the track of shortest travel time between given i... more The brachistochrone problem consists of finding the track of shortest travel time between given initial and final points for a particle sliding frictionlessly along it under the influence of a given external force field. Solvable variations of the standard example of a uniform gravitational field would be suitable for homework and computer projects by undergraduate physics students studying intermediate mechanics and electromagnetism. An electrobrachistochrone problem is here proposed, in which a charged particle moves along a frictionless track under the influence of its electrostatic force of attraction to an image charge in a grounded conducting plane below the track. The path of least time is found to be a foreshortened cycloid and its properties are investigated analytically and graphically.

European Journal of Physics, 2018

A mat consisting of round bamboo rods connected by strings perpendicular to their axes unrolls wi... more A mat consisting of round bamboo rods connected by strings perpendicular to their axes unrolls without slipping on a horizontal table. Video analysis is used to measure the position of the centre of the remaining roll as a function of time. It is found to accelerate with time due to the ‘rocket effect’ of the roll ejecting rods backward relative to itself. Mechanical energy is not conserved because of the inelastic collisions of the rods with the table. The fitted coefficient of restitution (COR) is 0.59±0.04 which is consistent with known values for wood on wood. In support of this explanation, progressively smaller values of the COR are found when the mat is unrolled on a flat woven rug and on a shock-absorbing pad. The level of analysis is appropriate to an undergraduate course in physical mechanics.

Journal of the Washington Academy of Sciences, 2017

Many researchers have discussed the optimum speed at which to walk in the rain to get the least w... more Many researchers have discussed the optimum speed at which to walk in the rain to get the least wet. This article looks at a related problem: if walkers or runners are indifferent to the rain, how drenched do they become during their journeys home? The semi-empirical answer employs basic introductory physics and biomechanics, as well as anthropometric formulas related to human-body ratios.

European Journal of Physics, 2017

The time required for a particle to slide frictionlessly down a set of ramps connected end to end... more The time required for a particle to slide frictionlessly down a set of ramps connected end to end can be minimized numerically as a function of the coordinates of the connection points between ramps and compared to the exact cycloidal solution of the brachistochrone problem. It is found that a set of just three joined ramps over a large range of geometrical aspect ratios has a descent time within 5% of the optimal cycloid. The special case where the particle starts and ends at the same height has sufficient symmetry that it can be analyzed analytically using algebra alone. The level of analysis is appropriate to an undergraduate classical mechanics course.

European Journal of Physics, 2016

It is shown that if you blow vigorously over a curved strip of paper, it levitates into the shape... more It is shown that if you blow vigorously over a curved strip of paper, it levitates into the shape of a catenary. This result quantifies a common classroom demonstration and is a pedagogically useful addition to other studies of catenaries in an intermediate classical mechanics course.

European Journal of Physics, 2016

A frictionless cart in the shape of a right triangle (with the vertical side forward) is elastica... more A frictionless cart in the shape of a right triangle (with the vertical side forward) is elastically impacted by vertically falling raindrops. The speed of the cart as a function of time can be analytically deduced as an exercise in the use of trigonometric and hyperbolic functions. A characteristic time defines the approach to a terminal speed which is a sizeable fraction of the speed of the rain. The treatment is accessible to a student in a calculus-based mechanics course.

Latin-American Journal of Physics Education, 2015

A general equation is derived for the point along a descending curved track that a particle (such... more A general equation is derived for the point along a descending curved track that a particle (such as a marble or model car) loses contact with the surface, in the absence of dissipation of mechanical energy. The object is assumed to start from rest at a point on the curve of zero slope. The launch speed and angle are calculated for the examples of a circular and a log-secant curve. The equation shows that a particle can never launch off a parabolic track, because it cannot attain the speed of a freefalling object skimming along the surface of such a track.

The Physics Teacher, 2015

The hearts of sports fans were stirred recently by the fastest-ever try scored in international r... more The hearts of sports fans were stirred recently by the fastest-ever try scored in international rugby. Welsh winger Dafydd Howells crossed the Fijian try line to
score a mere six seconds after Angus O’Brien had started the game with a kickoff, in one of the fixtures in rugby’s Junior World Cup played on June 2, 2014, in New Zealand. This startlingly quick score, though, is of interest to physics players as well as rugby players. Howells’ try serves as an intriguing way to involve students in one of the “core competencies” of physicists—to model events in the real world. And with the Rugby World Cup taking place in 2015 in England, and rugby sevens making its debut in the
2016 Summer Olympics in Brazil (U.S. teams have qualified for both events), rugby is increasing in popularity in America and is even gaining some coverage on television. Thanks to You-Tube, Howells’ try is readily available to serve as a laboratory experiment for students to analyze.

European Journal of Physics, 2014

A rider in a roller coaster lets go of a particle such as a small marble. How far does the marble... more A rider in a roller coaster lets go of a particle such as a small marble. How far does the marble travel horizontally from the point of release before hitting the ground, assuming the speed of the roller coaster is determined by conservation of mechanical energy starting from the highest hill up which it was pulled? Where should the marble be released along the track if one wishes to maximize the range of the marble? These questions constitute interesting variations on conventional problems in two-dimensional kinematics, appropriate for an undergraduate course in classical mechanics. Exploration of various shapes of tracks could form interesting student projects for numerical or experimental investigation.

Journal of Biosciences and Medicines, 2024

American Journal of Physics, 2024

European Journal of Physics

Latin-American Journal of Physics Education, 2022

Physics Education, 2021

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The Physics Educator, 2019

American Journal of Physics, 2021

Journal of the Washington Academy of Sciences, 2020

The Physics Teacher, 2020

European Journal of Physics, 2018

Journal of the Washington Academy of Sciences, 2017

European Journal of Physics, 2017

European Journal of Physics, 2016

Latin-American Journal of Physics Education, 2015

The Physics Teacher, 2015

European Journal of Physics, 2014

Journal of the Washington Academy of Sciences, 2019

In astrophysics, great attention is paid to self-gravitating spheres of fluids, which serve as mo... more In astrophysics, great attention is paid to self-gravitating spheres of fluids, which serve as models of stars and gaseous planets. Such models usually describe the fluids as comprising of a perfect gas. Here we explore a self-gravitating cloud of a real gas that comprises of hard spheres, a fluid modeled by the Carnahan-Starling equation of state. As such, we present a simple model that provides an application of real gases that might be of interest in the classroom, and which might find applications in the study of clouds of nonpolar gases, such as can be found in the interstellar medium.

Journal of the Washington Academy of Sciences, 2015

This article discusses the internal structure of a type of star first proposed by August Schmidt ... more This article discusses the internal structure of a type of star first proposed by August Schmidt in 1891, one that causes any light to enter it to move in a circle. An exact analytical solution of the equation of hydrostatic equilibrium is thus obtained. The solution is physically realistic, in the sense that the central density, central pressure, and total mass are all finite, while both density and pressure drop to zero at the outer radius of the star. In the core of the star, the pressure depends only weakly on density. The outer layers of the star can be well-approximated as isothermal.

Ni prezentas novan solvon de la ekvacio de hidrostatika ekvilibro. Se stelo posedus gaûsan densec... more Ni prezentas novan solvon de la ekvacio de hidrostatika ekvilibro. Se stelo posedus gaûsan densecon, ĝi havus finian mason, temperaturon, kaj premon. Ni komparas la stelon kun politropicaj modeloj.

Open Journal of Statistics, 2022

Body Mass Index (BMI), defined as the ratio of individual mass (in kilograms) to the square of th... more Body Mass Index (BMI), defined as the ratio of individual mass (in kilograms) to the square of the associated height (in meters), is one of the most widely discussed and utilized risk factors in medicine and public health, given the increasing obesity worldwide and its relation to metabolic disease. Statistically, BMI is a composite random variable, since human weight (converted to mass) and height are themselves random variables. Much effort over the years has gone into attempts to model or approximate the BMI distribution function. This paper derives the mathematically exact BMI probability density function (PDF), as well as the exact bivariate PDF for human weight and height. Taken together, weight and height are shown to be correlated bivariate lognormal variables whose marginal distributions are each lognormal in form. The mean and variance of each marginal distribution, together with the linear correlation coefficient of the two distributions, provide 5 nonadjustable parameters for a given population that uniquely determine the corresponding BMI distribution, which is also shown to be lognormal in form. The theoretical analysis is tested experimentally by gender against a large anthropometric data base, and found to predict with near perfection the profile of the empirical BMI distribution and, to great accuracy, individual statistics including mean, variance, skewness, kurtosis, and correlation. Beyond solving a longstanding statistical problem, the significance of these findings is that, with knowledge of the exact BMI distribution functions for diverse populations, medical and public health professionals can then make better informed statistical inferences regarding BMI and public health policies to reduce obesity.

Medicina Internacia Revuo, 2021

Body mass index (BMI) is frequently used in the medical sciences as a measure of adiposity. BMI i... more Body mass index (BMI) is frequently used in the medical sciences as a measure of adiposity. BMI is the weight (in kg) divided by the square of the height (in meters). In contrast, formulas for ideal body weight (IBW) exist that are linear in the height. Here we obtain new formulas for ideal body weight for height by choosing a more mathematically appropriate reference height. We compare the BMI and IBW formulas by means of the ANSURII database, and show that the IBW formula presented here leads to lower percentage discrepancies in the calculation of the IBW compared to previous formulas

Medicina Internacia Revuo, 2020

We construct a new formula for body surface area based on geometric means. This we show, by means... more We construct a new formula for body surface area based on geometric means. This we show, by means of Bland-Altman analysis and use of the Kolmogorov-Smirnov and Anderson-Darling tests, to be statistically equivalent to the arithmetic average of existing formulas. The result, the geometric mean formula (GMF) is the expression BSA = 0.00878108*W0 .434972*H^ 0.67844. We show also that body surfaces areas predicted by the GMF obey a lognormal distribution.

International Journal of Mathematical Engineering and Science, 2014

The standard harmonic balance method consists in expanding the displacement of an oscillator as a... more The standard harmonic balance method consists in expanding the displacement of an oscillator as a Fourier cosine series in time. A key modification is proposed here, in which the conservative force is additionally expanded as a Fourier sine series in space. As a result, the steady-state oscillation frequency can be expressed in terms of a Bessel series, and the sums of many such series are known or can be developed. The method is illustrated for five different physical situations, including a ball rolling inside a V-shaped ramp, an electron attracted to a charged filament, a large-amplitude pendulum, and a Duffing oscillator. As an example of the results, the predicted period of a simple pendulum swinging between −90° and +90° is found to be only 0.4% larger than the exact value. Even better, the predicted frequency for the V-ramp case turns out to be exact.

The Mathematical Gazette, 2013

Consider a six-sided die in which two opposite faces are squares and the other four faces are rec... more Consider a six-sided die in which two opposite faces are squares and the other four faces are rectangles. One can think of it as an ordinary cubical die that has been stretched or compressed along one axis. There is some probability that one of the two square faces will show uppermost after such a die is randomly tossed. For example, in the limit that the die is cubical, the probability that the original square faces come up is 1/3. Over 30 years ago, the question was asked what is the probability if the die is not cubical?

The Mathematical Gazette, 2013

Crux Mathematicorum, 2000

To produce the most difficult dartboard possible, we devise a polynomial-time algorithm. The prob... more To produce the most difficult dartboard possible, we devise a polynomial-time algorithm. The problem, and the algorithm, are show to be closely related to the traveling salesman problem.

Journal of Scholarly Publishing, 1998

De Sphaera by John of Sacrobosco was used as a textbook in astronomy in Europe for 400 years. The... more De Sphaera by John of Sacrobosco was used as a textbook in astronomy in Europe for 400 years. The development of the book and its subsequent sale show remarkable parallels with developments in textbook publishing today. Even when the book was losing its momentum, a 'new edition' with an introduction by Philip Melanchthon gave the volume new life.

Journal of Scholarly Publishing, 2020

Academia prizes interdisciplinarity. But what of publishing interdisciplinary journals? They hold... more Academia prizes interdisciplinarity. But what of publishing interdisciplinary journals? They hold the promise of appealing to two different disciplines yet run the risk of appealing to neither. Here we consider one interdisciplinary field, the medical humanities, and undertake a thought experiment: What questions should a publisher ask when considering the possibility of starting a new interdisciplinary journal?

A brief glimpse at what the phenomenally successful TV show has in common with university presses.

Journal of Scholarly Publishing, 2016

During the Reformation, books on theological matters easily fell afoul of the Anglican hierarchy ... more During the Reformation, books on theological matters easily fell afoul of the
Anglican hierarchy in England and the Catholic hierarchies of Continental
Europe. Both Anglican and Catholic churches devised means to ensure, where
possible, that manuscripts were reviewed for style and content prior to publication.
This church ‘pre-censorship’ and control of the publishing industry might
be interpreted as the beginnings of external peer review.

Journal of Scholarly Publishing , 2015

The publishing industry spends much of its time worrying about books—prices, print runs, discount... more The publishing industry spends much of its time worrying about books—prices, print runs, discounts, their scholarly arguments, level of publicity, and so forth. With such a range of concerns, it is easy to forget that at the heart of publishing, and every industry, are human beings. In this article, we look at the four cardinal virtues—prudence, justice, fortitude, and temperance—and argue that if we bear these in mind when working with our colleagues, the quality and sales of books and journals produced will increase.

Anglican Embers: Quarterly Journal of the Anglican Use Society, 2013

Journal of Scholarly Publishing, 2012

Publishing is going through a period of tremendous change. The same was true in the sixteenth cen... more Publishing is going through a period of tremendous change. The same was true
in the sixteenth century. This article explores how the publication of Robert
Recorde’s The Whetstone of Witte in 1557, in which the equals sign was used
for the first time, serves, along with his other mathematical books, as a model
for innovation.

Journal of Scholarly Publishing, 2000

Using the publication history of the Bible, among other titles, as an example, Lipscombe discusse... more Using the publication history of the Bible, among other titles, as an example, Lipscombe discusses the inherent problems of publishing collections of essays, festschrifts, conference proceedings, translations, and sourcebooks. Issues including the scholarly merit of such publications, the difficulties of editorial and production coordination, and the diminishing popularity of such book projects are addressed.

Journal of Scholarly Publishing, 1999

Trevor Lipscombe takes exception to the nostalgia that exists about the 'good old days' of schola... more Trevor Lipscombe takes exception to the nostalgia that exists about the 'good old days' of scholarly publishing. He takes a closer look at the books in this so-called 'Golden Age' of scholarly publishing and finds a lack of coherent strategy-- it seems that acquisitions editors and the marketing team preferred to let authors and booksellers come to them. This underachieving approach was supported by the high volume of copies ordered by libraries, But now that library orders have plummeted, university presses must become more than just elaborate book printers -- they must be creative to survive, and editors and marketers need to be aware of each other's concerns and must work together to create a viable product. Lipscombe concludes that the Golden Age of monographs might be over, but the Golden Age of publishing has arrived.

Journal of Scholarly Publishing, 1998

Trevor Lipscombe asks a simple and compelling question. Why do so few university presses publish ... more Trevor Lipscombe asks a simple and compelling question. Why do so few university presses publish mathematics and science books, whether they be new monographs or works in translation? He reminds us, with an ingenious example, that not everything that is published successfully need be understood immediately.

Journal of Scholarly Publishing, 1998

De Sphaera by John of Sacrobosco was used s a textbook in astronomy in Europe for 400 years. The ... more De Sphaera by John of Sacrobosco was used s a textbook in astronomy in Europe for 400 years. The development of the book and its subsequent sale show remarkable parallels with developments in textbook publishing today. Even when the book was losing its momentum, a 'new edition' with an introduction by Philip Melanchthon gave the volume new life.

Oxford University Press, 2021

How fast can you calculate? Would you like to be faster? This book presents the time honored tric... more How fast can you calculate? Would you like to be faster? This book presents the time honored tricks and tips of calculation, from a fresh perspective, to boost the speed at which you can add -- whether a couple of numbers, or columns so long an accountant may faint. Find out how to subtract, multiply, divide, and find square roots more quickly.

What's more, this book gives suggestions for how to find answers that are “good enough” for tricky tasks like dividing by 17. It includes brand new ways to multiply and divide irrational numbers such as pi, e, the square root of 2, and the golden ratio. It has sections devoted to ancient mathematics, and the techniques we can borrow from previous and other cultures, in order to calculate more quickly. Examples, some serious, some fun, come from everyday life or from history -- like hot dog eating competitions, the Vatican's cricket team, the molecular weight of the molecule with the world's longest name, and the amount of people taken by Henry VIII to arguably history's biggest party, the Field of the Cloth of Gold. In an age of timed multiple-choice questions, the swifter you can sum, or rule out wrong answers, the better you will do. If you love to play with numbers, this book will be recreational reading. And if you ever wonder whether simple arithmetic problems can crop up in everyday life, this book provides a fresh perspective.

This novel about a young man's intellectual and spiritual development was the first work John Hen... more This novel about a young man's intellectual and spiritual development was the first work John Henry Newman wrote after entering the Roman Catholic Church in 1845. The story describes the perplexing questions and doubts Charles Reding experiences while attending Oxford. Though intending to avoid the religious controversies that are being heatedly debated at the university, Reding ends up leaving the Church of England and becoming a Catholic. A former Anglican clergyman who was later named a Catholic cardinal, Newman wrote this autobiographical novel to illustrate his own reasons for embracing Catholicism.

Albert Einstein remains one of most famous scientists in world history. His image is instantly re... more Albert Einstein remains one of most famous scientists in world history. His image is instantly recognizable by even the most scientifically uninformed person―for many people, Einstein personifies genius. But who was Einstein really? What was he like as a person? What did his science actually mean? This fresh biography of Albert Einstein provides students and general readers a concise, accessible introduction to the life and science of this revolutionary man. Underneath his genius, Einstein was an ordinary person, with human frailties and weaknesses, but also with charm, modesty, a wry sense of humor, and idiosyncrasies. Readers will understand why he was named the Person of the Century by Time magazine.

Albert Einstein: A Biography will cover the entire history of this brilliant physicist's life and career, including: his early education, during which he was an excellent student, contrary to what is commonly believed; Einstein's struggles to find an academic position, which led him to work as a clerk at the Swiss patent office during the same period he was formulating his most famous and revolutionary theories; his troubled marriages and family life; Einstein's rise to international fame, and his use of that fame to fight for world peace; and Einstein's major contributions to physics, explained in ways that can be understood by anyone who wishes a fuller understanding of his scientific theories. The book includes a bibliography of secondary works that are useful for further reading, and a timeline of important dates in the life of Einstein.

What if Einstein played rugby? Surely Time Magazine's Man of the Century might offer useful tips ... more What if Einstein played rugby? Surely Time Magazine's Man of the Century might offer useful tips and techniques to defeat the opposition? In this book, the world of physics joins forces with the world of rugby, to show you how to tackle harder, pass safer, run faster, and scrum better - all the things you need to do to win. Blending simple physics, the kind you meet in high school, with anecdotes and stories from the world of rugby, Trevor Lipscombe takes us on a journey from scrum ruck and maul, to the running and passing of the offence, the chasing and tackling of the defence, through the kicking of penalties, to dressing for success in scorching summer sevens or winning in the winter. Physics at last comes alive, for here we look at a scrum, say, show what Newton's laws have to say about it, and then use the physics to see how to improve rugby. For any rugby fan with a smattering of science, or any science buff who knows the rudiments of rugby, The Physics of Rugby should delight, entertain, and instruct.

Catholic Home Educator, 2003

Catholic Home Educator, 2002

"Rugby is a good occasion for keeping 30 bullies far from the centre of the city." Oscar Wilde "... more "Rugby is a good occasion for keeping 30 bullies far from the centre of the city." Oscar Wilde

"I prefer rugby to soccer. I enjoy the violence in rugby, except when they start biting each other's ears off." Elizabeth Taylor.

The Physics of Rugby, 2009

"No leadership, no ideas. Not even enough imagination to thump someone in the lineout when the re... more "No leadership, no ideas. Not even enough imagination to thump someone in the lineout when the ref wasn't looking." JPR Williams

"Forwards are gnarled and scarred creatures who have a propensity for running into and bleeding all over each other." Peter Fitzsimmons

The Physics of Rugby, 2009

"Remember that rugby is a team game; all 14 of you make sure to pass the ball to Jonah." Anonymou... more "Remember that rugby is a team game; all 14 of you make sure to pass the ball to Jonah." Anonymous fax to the New Zealand rugby team.

"In 1823, William Webb Ellis first picked up the ball in his arms and ran with it. And for the next 156 years forwards have been trying to work out why." Sir Tasker Watkins VC GBE.

The Physics of Rugby, 2009

"Bloody typical, isn't it? The car's a write-off. The tanker's a write-off. But JPR comes out of ... more "Bloody typical, isn't it? The car's a write-off. The tanker's a write-off. But JPR comes out of it all in one piece." Gareth Edwards, commenting on JPR Williams's traffic accident.

"You've got to get your first tackle in early, even if it's late." Ray Gravell.

The Physics of Rugby, 2009

"Tony Ward is the most important player in Ireland. His legs are far more important to his countr... more "Tony Ward is the most important player in Ireland. His legs are far more important to his country than even those of Marlene Dietrich were to the film industry. A little hairier maybe, but a pair of absoulte winners." CMH Gibson.

"I didn't know what was going on at the start in the swirling wind. The flags were all pointing in different directions and I thought the Irish had starched them just to fool us." Mike Watkins.

The Physics of Rugby, 2009

"Do you know what? I'd give it all up tomorrow, the whole lot, for one Irish cap. Just one. There... more "Do you know what? I'd give it all up tomorrow, the whole lot, for one Irish cap. Just one. There is hardly a day that passes that I don't think of what it would be like to run out on to Lansdowne Road as one of the Irish team." Richard 'Dumbledore' Harris.

"Look what these &^&((( have done to Wales. They've taken our coal, our water, our steel. They buy our houses and live in them for a fortnight every twelve months. What have they given us? Absolutely nothing. We've been exploited, raped, and controlled and punished by the English. And that's who you are playing this afternoon." Phil Bennett's pep talk.

The Physics of Rugby, 2009

This is a book review of "Particles of Faith: A Catholic Guide to Navigating Science" by Stacy Tr... more This is a book review of "Particles of Faith: A Catholic Guide to Navigating Science" by Stacy Trasancos, which appeared in Saint Austin review 17(3) 2017, pp 36-38.

My review of Shagan and Shuger's "Religion in Tudor England" (Baylor University Press, 2016) whic... more My review of Shagan and Shuger's "Religion in Tudor England" (Baylor University Press, 2016) which appeared in St. Austin Review November/December 2016, Vol. 16(6) p.40-41.

Quick(er) Calculations, 2021

This chapter presents methods to add and subtract numbers more swiftly. These include breaking a ... more This chapter presents methods to add and subtract numbers more swiftly. These include breaking a subtraction or addition down into two, simpler steps. It also includes a way to add or subtract when the numbers involved fall on either side of a round number, such as 10, 100, or 1,000. These methods rely on two fundamental properties of numbers, namely the associative and commutative laws. Each of the methods presented contains a worked example. Furthermore, an intriguing property of three-digit numbers, involving “mirror numbers” and the number 1,089 is shown and proved. Fifty challenge problems conclude the chapter, to provide practice for the reader.