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How it Works »New Instructable »Hi! After looking on the net for calculations to predict the distance of a projectile launched by a trebuchet, I've not found anything useful. There are many variables and each one can be changed to alter the projectile distance and velocity. I am looking for a simple way to calculate this without calculus.Thanks again.?

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active| newest | oldestRange (max) = 2 * (m1/m2) * h

Now the efficiency of the trebuchet will cause this model to be off by quite a bit. But once you have a working trebuchet, we find this model works well when we vary m1, m2, or h. We assume we have a take off angle of 45 degrees above the horizon.

This solution is based on the classic max range ballistics problem - 45 degree take off angle. It also assumes converting all the potential energy of the counter weight to kinetic energy of the projectile. That is why the efficiency issue comes up as a lot of energy is lost due to friction in the moving trebuchet. If the projectile spins a lot then it will travel a shorter distance as the potential energy is split into kinetic and rotational energy. Projectile shape and wind will also vary the results.

The students found this worked well enough for their lab work and it was lot of fun. Good luck!

Thanks for the reply. I just noticed it today. The autonotify must not be working or getting caught in my spam folder.

Anyway, your solution appears VERY simple indeed!

I'll have to give a shot. So far this is the best answer and I'll select it as such.

It should be possible to do some sort of maximisation calculations, if you knew all the formula.

justfound your message.I'll check out your suggested website - sounds cool!

I did it on purpose to mess with the mathematically conscious. Of course, pi is an infinite, non-repeating decimal and all standard rules apply; I truncated instead of rounding.

Thank you for commenting Mr. Duck.

You (should) know the mass / weight of the counterbalance, and how far it travels during a shot. You should also know the weight / mass of the projectile, and how far

ittravels before release.Assuming a spherical horse in a vacuum, they can state that

work out = work in, and be able to calculate the KE of the projectile.If they also know the launch angle of the projectile, that should convert quite easily into a predicted range.

When they fail to meet the predicted range, they can then work out why, which would be equally as educational as building the weapon in the first place.

unbuilttrebuchet.. Let's see if we can at least help him determine which variables are most important.

- mass of projectile. If it's reasonably dense and semi-aerodynamic (eg, rock, bowling ball), you can probably ignore air resistance. Should be able to find a reasonable approximation of effective area and drag online, if wanted.
- torque of machine. This should just be a function of counter-weight mass and lever lengths. Depending on construction methods, friction may or may not be very important. Can probably use a fudge factor of, say, 10-20% loss.
- lengths of rigid arm and sling. I can imagine that computing the launch velocity, with the sling attached, will be rather complicated. This is where a web search would come in handy. I don't think the rigidity of the arm(s) will have that much of an effect (unless they are very flexible). Along the same line, with a suitably strong sling, I don't think stretch will be that big of a deal.

. With that data, one should be able to compute launch velocity. I'm not the one, but someone should be able to figure it out.. I have no idea how you would figure out the launch angle. Web search.

Work = force x distance

They (should) know the mass / weight of the counterbalance, and how far it travels during a shot. They should also know the weight / mss of the projectile, and how far

ittravels before release.Assuming a spherical horse in a vacuum, they can state that

work out = work in, and be able to calculate the KE of the projectile.If they also know the launch angle of the projectile, that should convert quite easily into a predicted range.

When they fail to meet the predicted range, they can then work out why, which would be equally as educational as building the weapon in the first place.

(I'm going to re-post that as a proper answer - Pi is a physicist, he'll know the relevant equations).

http://www.thehurl.org/tiki-download_file.php?fileId=9

These 2 PDF files probably have everything you need. They have a simple formula for calculating theoretical max range that depends only on the mass of the projectile, the mass of the counterweight, and one angle.

I'd keep it simple and focus on the basic physics -- projectile motion, principles of work and energy, and maybe efficiency.

You could also talk about the basics of mathematical modelling (formulate problem, develop model, test model, refine/simplify model.)

Anyway, thanks for putting effort into this for the students. I wish I had more teachers that did this kind of stuff when I was in High School...