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Physics of Batman: The Dark Knight

Batman Angular

Let’s assume that the memory fiber used in “The Dark Knight” is real, and that it can be used to change the shape of a cape into gliding wings with the application of an electrical current.  (No such material yet exists, but materials scientists may be getting close.)

Why don’t people use some form of bat wings? Let’s analyze the forces your arms would have to exert in order to successfully use bat wings.


Adapted from “The Physics of Batman: The Dark Knight – High Dive”, Adam Weiner, 08.15.2008

Batman spreads his wings & moves into a circular path.
His motion goes from vertical to horizontal.
The force of air resistance increases dramatically when he opens his wings.
This force turns his linear path into a circular path.
This inward pointing force is a centripetal force.

Law of physics: No object travels in a circular path (Newton’s 1st law), unless some force continually pulls it radially inward.

The balance of inertia and a radially inward force can create circular motion.

Centripetal force depends on the radius of the curve (r) and the radial velocity (v)

F = mv2/r

When a glider – or a Batwing – is bent into the wind, one can use the force to deflect the glider, plane or Batman.

Red arrow to upper right = “lift” (due to the wind hitting the wings)

Red arrow down = weight

Horizontal green arrow is the horizontal component of lift (aka centripetal force)

Vertical green arrow is the vertical component of lift. (If itis big enough, then one can glide for long periods of time)

What about Newton’s 3rd law of motion?

To hold his arms out, Batman has to exert the same force back on the air. So while he moves in a circle, we can calculate the force that will be exerted on Batman’s arms.

circle radius = 20 meters

man + equipment mass = 80 kg

speed remains constant during this turn

Let’s estimate the force on Batman’s arms as he sweeps through the bottom of the arc.

F = weight + centripetal force

F = m g + m v2/r = m ( g + v2/r )

= 80 kg (9.8 m/s2 + [40 m/s]2 /20 m) = 7200 N

= about 1600 pounds

This means that Batman has to hold 800 pounds on each arm!  Imagine lying on your back, on a workout bench, holding your arms out and having 800 pounds of weights placed on each one!  This is probably impossible for someone to do without super-strength.

Perhaps there is a way out of this. Maybe there are some hinges that connect the wings to the Bat suit. If so, then these hinges could be doing some of the supporting, rather than Batman’s arms.


Cartoon Laws of Physics

Cartoon Law I

Any body suspended in space will remain in space until made aware of its situation.

Daffy Duck steps off a cliff, expecting further pastureland. He loiters in midair, soliloquizing flippantly, until he chances to look down. At this point, the familiar principle of 32 feet per second per second takes over.

Cartoon Law II

Any body in motion will tend to remain in motion until solid matter intervenes suddenly.

Whether shot from a cannon or in hot pursuit on foot, cartoon characters are so absolute in their momentum that only a telephone pole or an outsize boulder retards their forward motion absolutely. Sir Isaac Newton called this sudden termination of motion the stooge’s surcease.

Cartoon Law III

Any body passing through solid matter will leave a perforation conforming to its perimeter.

Also called the silhouette of passage, this phenomenon is the speciality of victims of directed-pressure explosions and of reckless cowards who are so eager to escape that they exit directly through the wall of a house, leaving a cookie-cutout-perfect hole. The threat of skunks or matrimony often catalyzes this reaction.

Cartoon Law IV

The time required for an object to fall twenty stories is greater than or equal to the time it takes for whoever knocked it off the ledge to spiral down twenty flights to attempt to capture it unbroken.

Such an object is inevitably priceless, the attempt to capture it inevitably unsuccessful.

Cartoon Law V

All principles of gravity are negated by fear.

Psychic forces are sufficient in most bodies for a shock to propel them directly away from the earth’s surface. A spooky noise or an adversary’s signature sound will induce motion upward, usually to the cradle of a chandelier, a treetop, or the crest of a flagpole. The feet of a character who is running or the wheels of a speeding auto need never touch the ground, especially when in flight.

Cartoon Law VI

As speed increases, objects can be in several places at once.

This is particularly true of tooth-and-claw fights, in which a character’s head may be glimpsed emerging from the cloud of altercation at several places simultaneously. This effect is common as well among bodies that are spinning or being throttled. A ‘wacky’ character has the option of self- replication only at manic high speeds and may ricochet off walls to achieve the velocity required.

Cartoon Law VII

Certain bodies can pass through solid walls painted to resemble tunnel entrances; others cannot.

This trompe l’oeil inconsistency has baffled generations, but at least it is known that whoever paints an entrance on a wall’s surface to trick an opponent will be unable to pursue him into this theoretical space. The painter is flattened against the wall when he attempts to follow into the painting. This is ultimately a problem of art, not of science.

Cartoon Law VIII

Any violent rearrangement of feline matter is impermanent.

Cartoon cats possess even more deaths than the traditional nine lives might comfortably afford. They can be decimated, spliced, splayed, accordion-pleated, spindled, or disassembled, but they cannot be destroyed. After a few moments of blinking self pity, they reinflate, elongate, snap back, or solidify.

Corollary: A cat will assume the shape of its container.

Cartoon Law IX

Everything falls faster than an anvil.

Cartoon Law X

For every vengea nce there is an equal and opposite revengeance.

This is the one law of animated cartoon motion that also applies to the physical world at large. For that reason, we need the relief of watching it happen to a duck instead.

Cartoon Law Amendment A

A sharp object will always propel a character upward.

When poked (usually in the buttocks) with a sharp object (usually a pin), a character will defy gravity by shooting straight up, with great velocity.

Cartoon Law Amendment B

The laws of object permanence are nullified for “cool” characters.

Characters who are intended to be “cool” can make previously nonexistent objects appear from behind their backs at will. For instance, the Road Runner can materialize signs to express himself without speaking.

Cartoon Law Amendment C

Explosive weapons cannot cause fatal injuries.

They merely turn characters temporarily black and smoky.

Cartoon Law Amendment D

Gravity is transmitted by slow-moving waves of large wavelengths.

Their operation can be wittnessed by observing the behavior of a canine suspended over a large vertical drop. Its feet will begin to fall first, causing its legs to stretch. As the wave reaches its torso, that part will begin to fall, causing the neck to stretch. As the head begins to fall, tension is released and the canine will resume its regular proportions until such time as it strikes the ground.

Cartoon Law Amendment E

Dynamite is spontaneously generated in “C-spaces” (spaces in which cartoon laws hold).

The process is analogous to steady-state theories of the universe which postulated that the tensions involved in maintaining a space would cause the creation of hydrogen from nothing. Dynamite quanta are quite large (stick sized) and unstable (lit). Such quanta are attracted to psychic forces generated by feelings of distress in “cool” characters (see Amendment B, which may be a special case of this law), who are able to use said quanta to their advantage. One may imagine C-spaces where all matter and energy result from primal masses of dynamite exploding. A big bang indeed.

© 1997 William Geoffrey Shotts. Last update: Thursday, December 4, 1997

Hovercraft build project

Hovercraft project:Choose 2 of the 3 options

I. Build and demonstrate a hovercraft, or

II. Write a typed report, with a cover page, 3 double-spaced pages of text, and 1 page of citations/references, on what a hovercraft is, how they work, and how they use Newton’s laws of motion, or

III. Create a computer presentation on what a hovercraft is, how they work, and how they use Newton’s laws of motion. Present it to the class.

You may use software such as Microsoft PowerPoint, OpenOffice Impress, Corel Presentations, or any other software you like. All of these programs are very similar. OpenOffice is a package of programs very much like MS Office, but totally free. http://www.openoffice.org/

The entire project may be found in this document: TO BE ADDED

How to build your own hovercraft

Photos from a hovercraft project

Build a remote control hovercraft!

Can a hovercraft go up the walls?

A simple to build project

Mod your toy helicopter; turn it into a hovercraft

EGR 100 — Hovercraft Design Project: College freshmen majoring in engineering build and design hovercrafts


Hovercraft calculator – used only for building larger hovercraft that can actually carry passengers.




Your task is to build a mousetrap powered car, built from wood, paper, plastic, metal, erector sets, pens, rulers, old toys, Legos, or other materials.

We need a fair comparison between race cars. Therefore it must be powered by only 1 mousetrap. You may not modify the mousetrap, such as by over-winding the metal coil, because that would unfairly increase its potential energy storage.

A rat trap, or trap for any other animal, is not safe or acceptable.

2 people may collaborate to make 1 car.

If you do not have your car on the day that it is due, you lose 5 points per day. After 3 late days the project will not be accepted at all.

I suggest working in groups, making your own local mousetrap racer “factory”. This approach is easier and more fun.

Clearly print your names somewhere on the car!
Tue Sept. 15 – Introduce the project.

Thur Sept. 24 – Bring in your mousetrap racer, even if it is not yet completed. Compare your car with the cars made by others. Test it out, and see what modifications need to be made.

Tue Sept. 29 – Mousetrap racers due today. We will have competitions:

(A) Fastest: Which car goes to the finish line in the shortest amount of time?

(B) Furthest distance: Which car goes the furthest?

Much information on mouse trap racers is available online. However, you may not use a kit to build your racer.

Websites with information on how to make mousetrap cars:



Gallery of great mousetrap racers

What is a mousetrap powered car? How does it work?

It is a vehicle powered by a mousetrap spring. We tie one end of a string to the tip of a mousetrap’s snapper arm, and the other end of the string has a loop that is designed to “catch” a hook that is glued to a drive axle. Once the loop is placed over the axle hook, the string is wound around the drive axle by turning the wheels in the opposite direction to the vehicle intended motion.

As the string is wound around the axle, the lever arm is pulled closer to the drive axle causing the mousetrap’s spring to “wind-up” and store energy. When the drive wheels are released, the string is pulled off the drive axle by the mousetrap, causing the wheels to rotate.

How do you build a mouse trap powered racer?
There is no one “right way” to build a mousetrap powered vehicle. The first step to making a good mouse trap powered car is simple: put something together and find out how it works.

Once you have something working you can begin to isolate the variables that are affecting the performance and learn to adjust to improve your results. You build, you test and experiment, you change, and you do it all over again.

What’s the difference between a FAST Racer and a LONG distance traveler?

When you build a mouse-trap car for distance, you want a small energy consumption per second or a small power usage. Smaller power outputs will produce less wasted energy and have greater efficiency. When you build a vehicle for speed, you want to use your energy quickly or at a high power output. You can change the power ratio of your vehicle by changing one or all of the following:

* where the string attaches to the mouse-trap’s lever arm
* the drive wheel diameter
* the drive axle diameter.

The amount of energy released by using a short lever arm or a long lever arm is the same, but the length of the lever arm will determine the rate at which the energy is released and this is called the power output. Long lever arms decrease the pulling force and power output but increase the pulling distance. Short lever arms increase the pulling force and the power output by decrease the pulling distance but increasing the speed.

If you are building a mouse-trap car for speed, you will want to maximize the power output to a point just before the wheels begin to spin-out on the floor. Maximum power output means more energy is being transferred into energy of motion in a shorter amount of time. Greater acceleration can be achieved by having a short length lever arm and/or by having a small axle to wheel ratio.

If you are building a distance vehicle, you want to minimize the power output or transfer stored energy into energy of motion at a slow rate. This usually means having a long lever arm and a large axle-to-wheel ratio.

If you make the lever arm too long, you may not have enough torque through the entire pulling distance to keep the vehicle moving, in which case you will have to attach the string to a lower point or change the axle-to wheel ratio.


Most parts are scavenged from toys, or recycled materials. You may also consider stores such as Michael’s Art Supply, Home Depot, or A. C. Moore. Mousetraps are available in 2 packs, for less than $2, from all large supermarkets.

Suggested reading

I would be most content if my children grew up to be the kind of people who think decorating consists mostly of building enough bookshelves.

~Anna Quindlen, “Enough Bookshelves,” New York Times, 7 August 1991

I find television very educating. Every time somebody turns on the set, I go into the other room and read a book.

~Groucho Marx

The man who doesn’t read good books has no advantage over the man who can’t read them.

~ Mark Twain


At the Mountains of Madness, The Complete Works of Howard Philips Lovecraft, Arkham House, Wisconsin

Here are all the novels of Howard Phillips Lovecraft in one volume: At the Mountains of Madness, The Case of Charles Dexter Ward, The Dream-Quest of Unknown Kadath, The Shunned House, The Dreams in the Witch House, The Statement of Randolph Carter, The Silver Key, and Through the Gates of the Silver Key.

“1984” George Orwell.

A review at Amazon.Com states: Newspeak, doublethink, thoughtcrime – in 1984, George Orwell created a whole vocabulary of words concerning totalitarian control that have since passed into our common vocabulary. More importantly, he has portrayed a chillingly credible dystopia. In our deeply anxious world, the seeds of unthinking conformity are everywhere in evidence; and Big Brother is always looking for his chance. –Daniel Hintzsche

“The Annotated Hobbit”, J. R. R. Tolkien, Annotated by Douglas A. Anderson, Houghton Mifflin Company, 2002


Amir D. Aczel, “Probability 1: Why There Must Be Intelligent Life in the Universe”, Harcourt Brace

“Surely You’re Joking Mr. Feynman”, Richard Feynman, Bantam Books

“Secrets of the Supernatural: Investigating the World’s Occult Mysteries”, Joe Nickell with John F. Fischer, Prometheus books

“How To Think About Weird Things” Schick and Vaughn

Teaches us to think critically about the many New Age claims and beliefs that abound in our culture. In an examination of over 60 paranormal, supernatural, or mysterious phenomena, the authors focus on types of logical arguments and types of proofs. This is a versatile supplement for logic, critical reasoning, and philosophy of science courses.

“Quantum Reality” Nick Herbert, Anchor books.

This clearly explained layman’s introduction to quantum physics is an accessible excursion into metaphysics and the meaning of reality. Herbert exposes the quantum world and the scientific and philosophical controversy about its interpretation.

“The Sunflower: On the Possibilities and Limits of Forgiveness – Revised and expanded edition”, Simon Wiesenthal, Schocken

While imprisoned in a Nazi concentration camp, Simon Wiesenthal was taken one day from his work detail to the bedside of a dying member of the SS. Haunted by the crimes in which he had participated, the soldier wanted to confess to–and obtain absolution from–a Jew. Faced with the choice between compassion and justice, silence and truth, Wiesenthal said nothing.  But even years after the way had ended, he wondered: Had he done the right thing? What would you have done in his place?

In this important book, fifty-three distinguished men and women respond to Wiesenthal’s questions. They are theologians, political leaders, writers, jurists, psychiatrists, human rights activists, Holocaust survivors, and victims of attempted genocides in Bosnia, Cambodia, China and Tibet. Their responses, as varied as their experiences of the world, remind us that Wiesenthal’s questions are not limited to events of the past.  Often surprising and always thought provoking, The Sunflower will challenge you to define your beliefs about justice, compassion, and human responsibility.

“Religion and Science”, Ian G. Barbour, Harpercollins

“When Science Meets Religion” Ian G. Barbour, Harper SanFrancisco (Covers the same subjects as the above book, but in a shorter form)

The editorial review on Amazon.Com states that this “is a definitive contemporary discussion of the many issues surrounding our understanding of God and religious truth and experience in our scientific age.  This is a significantly expanded and freshly revised version of Religion in an Age of Science, winner of the American Academy of Religion Award for Excellence…[this edition adds] three crucial historical chapters on physics and metaphysics in the seventeenth century, nature and God in the eighteenth century, and biology and theology in the nineteenth century.”


“Lies My Teacher Told Me” James Loewen, Touchstone Books, New Press

Americans have lost touch with their history, and in this thought-provoking book, Professor James Loewen shows why.  After surveying twelve leading high school American history texts, he has concluded that not one does a decent job of making history interesting or memorable.  Marred by an embarrassing combination of blind patriotism, mindless optimism, sheer misinformation, and outright lies, these books omit almost all the ambiguity, passion, conflict, and drama from our past.  From the truth about Columbus’s historic voyages to an honest evaluation of our national leaders, Loewen revives our history, restoring to it the vitality and relevance it truly possesses.  Winner of the 1996 American Book Award and the Oliver Cromwell Cox Award for Distinguished Anti-Racist Scholarship

“Just and Unjust Wars” Michael Walzer, Basic Books

Is it ever ethical to fight a defensive war or an offensive war? If so, then under what circumstaces? Prof. Walzer takes us through the morality and immorality of many ancient wars, the two world wars, the Vietnam war, the Arab-Israeli conflict, the Persian Gulf war, and in the third edition of this book, the war in former Yugoslavia, Bosnia and Kosovo. “A classic treatment of the morality of war written by one of our country’s leading philosophers, with a new introduction considering the wars in Bosnia and Kosovo. Just and Unjust Wars examines a variety of conflicts in order to understand exactly why, according to Walzer, “the argument about war and justice is still a political and moral necessity.” Walzer’s classic work draws on historical illustrations that range all the way from the Athenian attack on Melos to this morning’s headlines, and uses the testimony of participants-decision makers and victims alike-to examine the moral issues of warfare.”

“Quantum Reality” Nick Herbert, Anchor books.

This clearly explained layman’s introduction to quantum physics is an accessible excursion into metaphysics and the meaning of reality. Herbert exposes the quantum world and the scientific and philosophical controversy about its interpretation.

“Science Under Siege” Michael Fumento, William Morrow & Co


In a book sure to stir controversy among liberals and conservatives alike, Fumento “proves conclusively that dioxin, videodisplay terminals, power lines, pesticides, and other products of modern technology are not the deadly threats to you and your family’s health that you have heard, while some touted solutions to the real environmental problems such as the fuel gasohol, are grounded not in good science, but in cynical, dollar-driven politics.

“Surely You’re Joking, Mr Feynman!” Richard P. Feynman and Ralph Leighton, W. W. Norton and Co.

The outrageous exploits of one of this century’s greatest scientific minds and a legendary American original. In this phenomenal national bestseller, the Nobel Prize-winning physicist Richard P. Feynman recounts in his inimitable voice his adventures trading ideas on atomic physics with Einstein and Bohr and ideas on gambling with Nick the Greek, painting a naked female toreador, accompanying a ballet on his bongo drums and much else of an eyebrow-raising and hilarious nature. A New York Times bestseller; more than 500,000 copies sold.


“The Health Robbers: A Close Look at Quackery in America” Edited by Drs. Stephen Barrett and William Jarvis. Prometheus Books

The most important and comprehensive book about quackery ever published. Covers chiropractic, homeopathy, naturopathy, acupuncture, faith healing, vitamin pushers, mail-order quackery, “fad” diagnoses, overselling of herbs, cancer and arthritis quackery, unproven “allergies,” dubious dentistry, multilevel marketing, immuno-quackery, “organic” foods, weight-control facts/fads, occult practices, holistic hodgepodge, prominent promoters, why quackery persists, what can be done, and more. Some chapters of this book, and related information, are available online at:


“How To Think About Weird Things” Schick and Vaughn

Teaches us to think critically about the many New Age claims and beliefs that abound in our culture. In an examination of over 60 paranormal, supernatural, or mysterious phenomena, the authors focus on types of logical arguments and types of proofs. This is a versatile supplement for logic, critical reasoning, and philosophy of science courses.


“The liver does many jobs, but here are three big ones: It cleans your blood. It produces an important digestive liquid called bile. It stores energy in the form of a sugar called glycogen.”

Kidshealth.org – Liver


Sample questions

Laboratory tests can be used to evaluate how well a person’s liver is working. One test measures how well the liver removes a substance called bilirubin from the blood. Based on this information, which of the following describes bilirubin?
A. an antibody
B. an energy source
C. a vitamin
D. a waste product

Learning Standards



I: adapted from Giancoli Physics

Waves spread as they travel. When waves encounter an obstacle, they bend around it and pass into the region behind it. This phenomenon is called diffraction.
Wave diffraction
The amount of diffraction depends on the λ (wavelength) of the wave and on the size of the obstacle:

Water waves diffraction

(a) λ is much larger than the object. Wave bends around object almost as if it is not there.

(b) and (c) the λ is shorter than the size of the object. There’s more of a “shadow” region behind the obstacle where we might not expect the waves to penetrate — but they do, at least a little.

(d) the obstacle is the same as in part (c) but the λ is longer. More diffraction around object.

Rule: Only when λ is smaller than the size of the object will there be a shadow region.


II. Here we see water waves undergoing diffraction around an island.




Sound waves can diffract in unusual and unexpected ways. See our article on anomalous sounds

Even light itself can diffract!  See our article on light’s wave nature.

Giancoli Physics, Chap 24, The Wave Nature of Light


Real life application: Diffraction in Boston Harbor

spectacle Island Boston Harbor

from bostonfoodandwhine.com

As part of the Central Artery/Tunnel project – the Big Dig – Applied Coastal Research and Engineering did research on wave diffraction in Boston Harbor, around Spectacle Island.

…A detailed beach nourishment design was developed for the southern shoreline of Spectacle Island, which is located within Boston Harbor…  The propagation of waves from Massachusetts Bay into Boston Harbor was modeled using the refraction/diffraction model REF/DIF1. This model predicts the transformation of waves in areas where bathymetry is irregular and where diffraction is important, such as at Spectacle Island. The resulting wave heights, periods, and directions were used as input to both longshore and cross-shore sediment transport models. These models were employed to simulate the performance of several different beach fill designs…

Beach Nourishment Design for Spectacle Island

Spectacle Island Boston Harbor Diffraction

Boston Harbor Islands map

This map is from mass.gov/eea/images/dcr

Learning Standards

2016 Massachusetts Science and Technology/Engineering Curriculum Framework

HS-PS4-1. Use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves traveling within various media. Recognize that electromagnetic waves can travel through empty space (without a medium) as compared to mechanical waves that require a medium

SAT subject test in Physics: Waves and optics

• General wave properties, such as wave speed, frequency, wavelength, superposition, standing wave diffraction, and Doppler effect
• Reflection and refraction, such as Snell’s law and changes in wavelength and speed
• Ray optics, such as image formation using pinholes, mirrors, and lenses
• Physical optics, such as single-slit diffraction, double-slit interference, polarization, and color