At what point does model rocketry have to morph into HPR?

[OC_Rocket_Man]

F = ma is certainly applicable, but since acceleration is defined as delta-v over delta-t, the "F = ma" equation displays asymptotic behavior as delta-t approaches zero. To put it more simply, as the time it takes for an object to decelerate approaches zero, the amount of force required to achieve that deceleration approaches infinity. If we modeled the behavior of an object falling at any velocity and hitting the ground as an instantaneous deceleration to zero, we would run into the infinite force issue. That's one of the reasons why that equation doesn't really help in determining what happens when a moving object hits something like the ground or a person's head.

Yes, you need to convert dynamic energy into impact work.

Fmax = 2 (M)(V) / (slow down distance)

 

[jlabrasca]

Ok, thanks.

How then is the "Force" of an impact defined and calculated?

There a couple different ways to compute the average force exerted on the rocket (or on the thing struck by the rocket) at impact. In terms of the work done accelerating the rocket to rest it would be the change in energy for the rocket divided by the distance traveled during impact. You might also work it in terms of the change in momentum (impulse) divided by the duration of the collision. These are equivalent. Momentum and energy are simply related and a change in one will result in a corresponding change in the other.

Already regretting this...

The OP has been silent since the top post, but maybe we can try to parse the questions into a problem statement (snipping a bit)

... the last few kits I bought were fiberglass, carbon fiber, and metal tipped nosecones. Some of these "indestructible" kits are even designed for short-thrust E, F, and G motors...I've seen too many over-engineered and under-executed, "indestructible" rockets plant themselves balls-deep into the ground. I have to think that if that same lawn-dart hit an RV, car, or person it wouldn't be pretty...Why use fiberglass instead of paper tubing? Why use a metal-tipped nosecone instead of a plastic cone?

I'll leave it to the reader to demonstrate that those two expressions for the average force are the same. <grin>

The issue under discussion appears to be that the skull and its contents do all of the work of stopping the rocket. That is to say, the skull deforms (undergoes a plastic strain to the point of rupture) to dissipate the energy of the falling rocket. The stress which produces this strain is the force per unit area acting between the two bodies during the collision. The force is exerted by the skull on the rocket. The area is the area of contact between the skull and the rocket.

There is an upper limit to the stress that can be exerted by the skull -- called its ultimate strength (at least, thats what it is called in physics classes, mech. engineers might call it something else). Penetration occurs when this limiting stress is exceeded.

If the rocket body was not rigid and hardened against deformation, some of the energy would be dissipated by the crumpling of the body tube/the duration of the collision would increase/the distance travelled by the center of mass of the rocket would increase, and the force acting between skull and rocket would decrease.

A deformable nosecone might also flatten at impact, increasing the contact area and decreasing the stress exerted by the skull (and on the skull).

A separate, but related issue -- discussed upthread -- is that the materials used to harden the rocket are also likely to produce a heavier rocket (for a given geometry) which will be moving faster at impact, so that a greater force will be required to accelerate it to rest.

 

[lakeroadster]

This thread has wings... :flyingpig:

The skull looks happy!