EEK! = MC2..or…the Mathematics of Haunting

Article by: Jason Wilson

 

I am sure that if any of us can remember back to our school days, we could recall hearing someone utter the words “I’ll never need to know this when I grow up.”…we may have even said those words ourselves.

But, even running a haunted house, you often use a lot of math…especially if you build your own props.  I’d like to take a moment to look into the mathematics of haunting and hopefully inspire our younger haunters that are still in school to pay a little more attention in class, so that they can be smart and effective haunters well into the future.

Now, there are several different “jobs” in the haunt industry from actor to prop-builder and while not all of them require math, a lot of them do.  I mean, really, you don’t need to know the square root of PI to jump out and scare someone.  But, let’s take a look at a few that do.

First off, what about being a mask maker.  You wouldn’t really think that sculpting clay and pouring latex would require much math…but it does.  To be efficient and make money, you want to avoid wasting materials and ordering a bunch of supplies that you don’t really need.  This is where math rears its head.  Being able to closely estimate how much material you will need, will save you a lot of money.  The clay, resins and latex used in creating top quality masks are not really cheap and some of the alginates that are used will not last forever.  So, how do you know how much you will need?  Most of the materials tell you how much area they cover.  Expanding foam resins will give you an expansion rate…or how much bigger it will be when it dries.  But, how do you know how much you need?

Well, let’s say that you want to make a fake arm out of latex.  The human body, while very complex in detail, can be broken down into some very basic shapes; a sphere for the head…cylinders for the torso, arms and legs…and a cone for the hip/groin area.  Knowing this…we know that we are looking at a cylinder as a base for our fake arm.

Now, we want to make it a solid latex/rubber prop…so, we need to know the VOLUME of the arm.  But, how do we figure out the volume of an arm? Easy…with math (you knew that was coming didn’t you). The mathematic equation for determining the volume of a cylinder is this:

V = ∏r2h or, Volume = PI x Radius2 x Height

 So, take out a ruler and hold it against your bicep.  Look at how wide it is from the top of your bicep, to the bottom of your arm and divide this measurement in half.  This will be our RADIUS.  To get our HEIGHT just measure from your shoulder to the tip of your middle finger.

We’ll say that our bicep/radius measurement was 4” and our height was 24”.We now have all three measurements that we need to figure out the volume of material we will need to make our arm.  Let’s put it to work.

Volume = PI x Radius2 x Height

 Volume = 3.142 x 42 x 24

 Volume = 3.142 x 16 x 24

 Volume = 1206 inches2

 So, we need enough latex to fill a 1206 in2 cavity.  Even though many places will give you the measurements in metric units (millimeters, liters), the math is still the same.  There are several websites on the internet that will do the metric conversions for you, so even if you don’t know how the whole standard to metric thing works out…don’t sweat it.

 Okay, so we see that you need math for mask making…but what about building other props?  Well, if you want them to move…you have more math ahead of you.

 Imagine that you want to make a prop that moves. For now, we’ll avoid full blown animatronics and robotics.  There is more math involved in that, than I have patience to discuss in this article.  We are just going to build a simple prop that moves back and forth.  Sounds easy right?  But, what kind of motor or actuator will you use to accomplish this?  If you have an air compressor handy, you can buy a linear actuator and your problem is solved.  However, we’ll say that we don’t and that we will be using an electric motor to make this thing move. 

A quick word on motors: Motors will have a “rating” for what voltage and amperage they can handle.  Using values greater or less than these ratings can damage the motor over time.  That being said…the simplest way of controlling a motor is through modifying its input voltage and amperage whereas a change in voltage will result in a change in speed and an amperage change will affect the “power” of the motor (how much it can push).

 A “wiper motor” is the most commonly used motor in prop-building.  But wait…a wiper motor spins in a circle…it doesn’t move back and forth!  Oh no, we are done for, there is no way we can make this work now! Or can we?

 Of course we can!  But first we want to know how far we want our prop to move back and forth.  So…decide now….go ahead, I’ll wait…do you have it?  Okay, we are going to make this thing move back and forth one foot.  I’ll spare you the boring and relatively unnecessary discussions about the coefficient of sliding friction…and just give you the important stuff.  After all, we aren’t building these things for NASA.

 We just need to figure out how to convert rotational motion into linear motion.  This involves an area of math known as Angular Kinetics.  Sounds scary, I know…but it isn’t very hard at all…in its simplest form.  We said that we wanted our prop to move one foot forward and back.  The easiest way to achieve this would be to attach one end of an arm that is six (6) inches long onto the spinning shaft of the motor.

circle_trig

WAIT A MINUTE…HOLD THE PHONES!!! If we want it to move twelve inches…why in the world would we only use a six inch arm?  Well, think about it this way…when the motor is turned on, it will cause the arm to move in a circle. This means that our arm just became the RADIUS distance of our circle.  In case you forgot, the radius of a circle is just a fancy way of saying “half its width”. As such, our circle’s entire width is twice the radius…or…TWELVE inches!

 

Now all we have to do is connect another arm from this one to the back of our prop.  However, this arm must be connected in such a way to keep it from actually spinning.  Drilling a hole through the ends of both arms and sliding a bolt through with a nut on the end…just tight enough to keep the two arms from coming apart…would do this for us.  There you have it…twelve inches of linear motion from a rotational motor.

See…that wasn’t so hard was it? 

Stay tuned…we will delve deeper into the mathematics behind haunting in Part 2.

4 Responses to “EEK! = MC2..or…the Mathematics of Haunting”

  1. Hi, nice post, i appreciate that you are encouraging people to learn math and being a math student, its nice to see your gesture. Carry on!

  2. Jason Wilson says:

    As a mechanical and electrical engineer by schooling and an amatuer physicist by hobby…I enjoy find the math and science behind everything around me. Math is an important part of all of our lives and one that is often overlooked by the majority.

    Thanks for the comment!

  3. Alice Kruse says:

    As a biologist by schooling, all this electrical stuff is Greek to me! Thank you for your breakdown and especially the graphics, which make the whole thing very clear. Will you explain later how to modify the voltage of a motor?

    Now to get a couple of wiper motors and play!

  4. Jason Wilson says:

    Thank you…I am glad it helped. I will make sure to cover the motors next!

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