In my previous share on the black arrow of the hobbit, I looked at the speed of some real fire stock in my backyard. Oh, in case you have not read this post, the shot arrow in the movie version of the Hobbit dislocation of Smug goes just around the speed of the Nerve Dart. Not very effective.
One colleague raised an interesting question. How much of the work you put into drawing back arch goes to the kinetic energy of the stock? He seemed to think it was not super high. Let's find out.
Oh, I can probably just look this online - but what fun is it?
Work while printing back A bow
How much work do I do when I draw the string back on the bow? If the power is fixed, I can only use the following definition of work.
Here F is the force that you pull with, rr is the displacement of this force and θ is the angle between force and displacement.
It does not take constant force to pull the bow. No, the farther back pull the harder series is pull. But what is the relationship between distance and power? There is only one way to learn - experience.
I have used my children's bow and heavy duty spring scale to pull the chain. Here is my setup.
From this, I get the following data.
I did not expect this to be a linear job. I'm not sure what I'm exacted - but not just linear. This plot appears to indicate that this bow works just like a spring that obeys the Hooke's Law:
In this expression, k will be the spring constant (with a value of 272 N / m) and s is the distance that is pulled back.
But what about the work done? Here, we can use a nice little trick. If you pull the chain back 10 cm, the force goes from 0 Newton to 27.2 Newton. Since this power changes linearly with displacement, I can only use the average force on this displacement - or s / 2. Therefore, in general, the work that was done in pulling the return chain s distance would be:
You have already specified a value for k. I can get an estimate of the energy stored in the bow if I only know how far it was pulled back.
KINETIC ENERGY OF AN ARROW
I already looked at more than one arrow shot in my "shooting the dragon" post. Here is another one.
From a video like this, I need two things. I need the distance the string is pulled back then I need the final speed of the stock. Wait, I need one more thing - block the arrow. The share used in these tests was a mass of 34.3 grams.
Well, let's get to the data. I have many videos with arrow clips. Each video with a different child that pulls the chain a different distance. After measuring both the speed of the arrow and the drawing length, I can make a plot of kinetic energy versus work done on the arc. Here is that plot.
Yes, there is a minor problem with this data. One arrow view is with a much larger "undo" than the others - that one I had. It would be nice to have more "in the middle" retreat shots, but okay.
Does this plot give us the answer? Think. The data looks fairly linear with a slope of 0.548. This means that if the chain pulled out and used 100 joules of work, about 54.8 jolls would go to the kinetic energy of the stock. But where does the rest of the energy go? The "lost" energy probably goes to the same bow. When you leave the arrow, this bow also starts to move. This is the energy there. But how can you make a bow more efficient? I suspect that something like a composite arch does not lose a lot of energy.
