# Throwing Spear – Part 2

Posted on January 12, 2010

LINK: Part 1

IN THIS PART: I’ll talk about types of spears and rotational mechanics.

First let me say thank you to the numerous people who directed my attention to the very important invention of the atlatl.  My intention is to build a hand-thrown spear, but it’s certainly important to learn about the atlatl.  So that’s where I’ll start in this post.  An atlatl is a spear-thrower.  It helps a human to throw faster by using leverage.  In essence, it extends the length of the thrower’s arm.  It also pushes the spear (or arrow or dart) from the back end rather than gripping it like a human hand would.  The result is that the thrower can accelerate the spear over a much greater distance before “letting go”.  That means it ends up going much faster.

Atlatls were definitely in use during the paleolithic era and they were a major advancement.  The optimal spear shape, weight, and weight distribution would not be the same for atlatl throwing as for the hand throwing I’m designing for.  Here is a link to a video someone made of atlatl use in slow motion: http://www.youtube.com/watch?v=DWdKW6c6uyU.  For more information about atlatls, check out the Wikipedia article: http://en.wikipedia.org/wiki/Atlatl.

Although it might fall into the category of common knowledge, it’s probably worth mentioning that some spears are not meant to be thrown at all.  Such spears are generally driven into the target with contact force from the user’s hand(s).

When it comes to the history and numerous varieties of spears, I think the best thing I can do is, once again, direct you to the Wikipedia article: http://en.wikipedia.org/wiki/Spear.  But here I will briefly summarize what a spear is.  It’s basically a long pole with one sharp end.  The sharp end is used to pierce a target.  I will talk in more detail about the features of spears, but before I can do that, I have to go through some more physics.

Picking up where I left off…  Imagine a rigid body, say an apple, spinning at a constant rate.  What kind of path is each one of the particles in the apple following?  The answer is: a circular path.  And each particle can’t just pick any old circular path to follow.  If they did, the apple might not hold its rigid shape.  The particles must rotate together around a common axis of rotation.  Imagine sticking a skewer through the apple and then rolling the skewer in your fingers.  The skewer runs along the apple’s axis of rotation.  But to get the apple spinning you have to get the individual particles moving along their circular paths.  That means the particles’ velocities will go from zero to something else – they will accelerate.  And remember that acceleration is the $a$ in $F = ma$.  The equation tells us that the particles, having non-zero mass, cannot accelerate until a force is applied to them.  And the force is proportional to the acceleration.  We also know that particles farther from the axis of rotation will have to accelerate faster because at any given velocity those particles would have to travel along a bigger circle in the same amount of time (one rotation).

It may be worth mentioning that even when the apple is spinning at a constant rate, its particles are being accelerated just so that they can keep moving in a circle rather than flying off in a straight line.  But that force is supplied by the chemical bonds within the apple, not by the turning of the skewer.  So we can pretty much forget about that part.  And when we do forget about that part, which is implied by calling the apple a rigid body in the first place, it becomes easier to talk about the rotation of the apple as a whole using a new equation which is very similar and analogous to $F = ma$.  The equation is $\tau = I\alpha$.  $\tau$ represents torque, which is the rotational analog of force.  Where force is how hard something is pushed or pulled, torque is how hard something is twisted.  $\alpha$, as you might guess, is the rotational analog of acceleration – referred to as angular acceleration.  And $I$ is a rotational analog of mass, called moment of inertia.  Moment of inertia is determined by the masses of all the particles combined with their distances from the axis of rotation.  But generally speaking, the heavier an object is the higher its moment of inertia.

I told you that everything would be based on $F = ma$ and I wasn’t lying.  These new concepts (torque, angular velocity / acceleration, moment of inertia, and the relationship between them) are all derived from those first principles.  In the study of mechanics there are many such concepts.  Some of the more well know ones are energy, momentum, and power.  In order to optimize my throwing spear, I’ll want to take a look at momentum.  But that’s for the next part!

IN THE NEXT PART: I’ll explain why momentum matters and examine some of the design tradeoffs for hand-thrown spears.

Thanks for reading!

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