Fun science question regarding the mechanics of a propelling mechanism

[Kyriakos]

What kind of accuracy can one hope for, in projectile movement where the propelling force is based on rubber band(s), if the target has to be at least twenty meters away? Tied to this, what would the happy medium be, regarding size of the mechanism and minimum of needed original force, assuming the cylindrical "ammo" is again weighing at least 50 grams?
Other things to take into account: target (can be regarded as stationary) is considerably higher than the point of attack (3-5 meters).
(this is for a story idea; I don't mean to actually build it ^^ Tbh I am mostly involved in the parts establishing the distance - angle of elevation etc - but the application of calculus has to be believable; besides, it is fun)


To be fair, the questions would have been diminished to just the first one (what accuracy, if rubber bands are used), if it wasn't for the logistical problems with a larger propelling mechanism (due to weight of ammo). Besides, in the story you don't have the luxury of failing to hit the target the first time you try to (it's not stationary there; is only expected to remain so while unaware).

[paleologos]

I fail to see how accuracy would depend on the method of energy transfer.

In the case of archery, an arrow whose shaft flexes is more accurate than an arrow whose shaft is stiff, even if they are fired by the same bow.
The reason for that is that the combination of fletching and shaft vibrations causes rotation of the projectile along the axis of movement, granting rotational momentum and ultimately gyroscopic stabilization.

Then, of course, there is the matter of what guides are used.
For example take into account solenarion archery. (Link1, Link2, Link3)

But most importantly, how do you measure accuracy and can you differentiate it from precision? (Link)

Spoiler Alert, click show to read: 

[Kyriakos]

My background isn't in physics (obvious ^^), so didn't know of the gyroscopic stabilization. But the main question is whether for relatively heavy ammo, you can hope to construct a rubber-band based mechanism if you don't have access to material outside those commonly found in an apartment block.
I mentioned rubber bands because I felt (?) that different basic transfer methods would be even harder to manually operate. For example, rope tension (eg ballista) very likely would make this impossible to fire, with any speed.
The story/plot is just about basic calculus, but it won't help if engineering-wise the thing is just inoperable - either due to unrealistically large physical force needed to shoot, or lack of force of the projectile, or terribly low accuracy (=>the mathematical planning on paper doesn't factor massive loss due to the material properties)

[paleologos]

It is perfectly possible to propel a projectile with rubber bands.
It is not possible to predict the precision and accuracy (yes they are different metrics) without having the actual contraption made.
Maybe you need something like that: Precision Slingshot

[swabian]

What kind of accuracy can one hope for, in projectile movement where the propelling force is based on rubber band(s), if the target has to be at least twenty meters away? Tied to this, what would the happy medium be, regarding size of the mechanism and minimum of needed original force, assuming the cylindrical "ammo" is again weighing at least 50 grams?
Other things to take into account: target (can be regarded as stationary) is considerably higher than the point of attack (3-5 meters).
(this is for a story idea; I don't mean to actually build it ^^ Tbh I am mostly involved in the parts establishing the distance - angle of elevation etc - but the application of calculus has to be believable; besides, it is fun)


To be fair, the questions would have been diminished to just the first one (what accuracy, if rubber bands are used), if it wasn't for the logistical problems with a larger propelling mechanism (due to weight of ammo). Besides, in the story you don't have the luxury of failing to hit the target the first time you try to (it's not stationary there; is only expected to remain so while unaware).

The method of delivery matters with regard to accuracy when it comes to vibrations in the catapult mechanism (whatever that is) and the projectile of course. The projectile will have spin, if it's not a solid sphere it can cause significant inaccuracy simply by its spin alone. If the projectile is not homogenous, elastic and spinning you will have the worst case, so simply assume a small steel bullet with spherical shape to eliminate all that. Is there a reason for it to be cylindrical? I'd expect a cylindrical shape to impair accuracy. All of this is a bit moot however, since the moost important determinant for both accuracy and precision in the sense paleologos suggested would be the personal skill of the shooter.

Yeah and obviously a catapult system involving a rubber band would be a slingshot, as palaeologos said. So it makes sense to google for slingshot accuracy.

As for trajectory calculation, the initial velocity of the projectile as well as its mass have to be measured. There might be calculators you can find online regarding the trajectory properties, like this one: https://www.geogebra.org/m/rYmNxYMY

Otherwise the trajectory is discussed here: https://en.wikipedia.org/wiki/Projec...the_trajectory

The optimal angle for maximum range is always 45° assuming 0 air resistance. If air resistance is considered, it's slightly lower than that, but i think this can be neglected.

[Kyriakos]

Thanks. My main intention is to incorporate the (known) equations in a literary enough style. But it wouldn't do if actual properties of the material (ie stuff you find in physics, not typically in math) make it impossible to succeed.
As for the ammo being "cylindrical", it's just far more believable that largely cylindrical objects were found in the place (even wooden pieces, which could form a spike on the end), rather than anything resembling a sphere (while still being heavy enough to do any damage to something pretty large, without needing some very powerful delivery system for initial velocity).