Physics of shooting a rifle - G force on a scope

[tangolima]

I dropoed a rifle scope from a 3ft high bench. It landed on concrete floor objective end first, bending the aluminum tube in front of the lens inward a bit. Other than that it seemed ok.

One side of my brain said "The scope is a goner", the other side said "It is .50BMG rated, so should be fine".

What exactly does .50BMG rated mean? How many Gs are we talking about?

Say, 800gr bullet going at 2900fps. 45" long barrel. Gun weighs 20lb. Peak pressure 55kpsi.

How many Gs of peak acceleration does that gun impose on the optics? How long is the approximate barrel time?

If my poor scope takes the same length of time to stop when it hits the ground, how many Gs did it receive? Do I need to worry about breakage?

-TL

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[JohnKSa]

If my poor scope takes the same length of time to stop when it hits the ground...

It stopped in a very short distance when dropped. You can measure the distance it took to stop by seeing how much the metal deformed. That's still not the whole story because the scope probably bounced as well.

Neglecting the bounce, the force applied to the scope (and to the floor) is the kinetic energy of the scope immediately before impact divided by the distance that it took for it to come to a stop.

[Nathan]

They aren’t really related. Scope recoil testing is very axial and held securely in a jig.

Dropping a scope is perpendicular to the recoil axis and exposes the scopes weakness in that a dropped scope hits at a specific point causing a super high stress concentration at that point.

The actual stress is a function of acceleration of slowing it to a stop. This is related to the compliance of the scope tube and ground. Both of those are pretty hard, but the tube yielded until the decelerating force could be held.

All this to say scopes suck at drop testing and need to be tested by scope companies with rifle attached. They generally don’t do this, so generally dropped rifle ruins a hunt. Hmm. Should scope makers test this? YES.

[tangolima]

The scope sort of hit the ground at 45 degree. I had no idea how much time it took to stop. But for the sake of discussion I just assume the same as a gun going off, or at least similar order of magnitude.

I went through the calculations. .50BMG is not as big a deal as it sounds.

BTW, the scope is ok other than the dent. It is a hunting scope with capped turrets and duplex reticle. It was on a SMLE with a no-drill mount. That stupid mount, that depended on a set screw to tension on the action, came loose after some firing. The whole thing just dropped. Needless to say group started to open up rather badly right before it happened.

-TL

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[tangolima]

Originally Posted by JohnKSa

It stopped in a very short distance when dropped. You can measure the distance it took to stop by seeing how much the metal deformed. That's still not the whole story because the scope probably bounced as well.



Neglecting the bounce, the force applied to the scope (and to the floor) is the kinetic energy of the scope immediately before impact divided by the distance that it took for it to come to a stop.

That's a slightly different angle to look at it. It works. The very end of the tube caved in by about 1/8". It hit the ground at 45 degree ish angle.

-TL

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[JohnKSa]

The calculation actually gives the maximum possible force that could have been applied by the drop.

If the scope hit at a significant angle it is more complicated because the scope didn't really stop on initial impact. The top of the scope would have kept moving even after the portion that impacted the ground initially had stopped. So not all of the kinetic energy was expended in the initial impact. Some was used to torque the scope, and then the rest of it was expended in the "secondary impact" when the top of the scope hit the ground.

Also, real world objects can suffer significantly different amounts of damage depending on how the object hits. Scopes, for example, tend to be made to handle force along the horizontal axis of the scope since that's how recoil affects them. Abrupt force applied at a significant angle to the horizontal axis of the scope could be much harder on the scope than the forces it was engineered to handle.

The same type of result (with the same caveats) can be obtained using the time (instead of the distance) it takes for the scope to stop and the momentum of the scope immediately before impact (instead of the kinetic energy). Of course, determining the time it took the scope to stop on impact is harder to determine without high-speed video of the event.

[davidsog]

They aren’t really related. Scope recoil testing is very axial and held securely in a jig.

Dropping a scope is perpendicular to the recoil axis and exposes the scopes weakness in that a dropped scope hits at a specific point causing a super high stress concentration at that point.

The actual stress is a function of acceleration of slowing it to a stop. This is related to the compliance of the scope tube and ground. Both of those are pretty hard, but the tube yielded until the decelerating force could be held.

This is correct.

Load factors limits are applicable to one axis only. Asymmetrical loading subjects the object to multiple axis loading often leading to structural failure far below the single axis rating.

That fact has killed many a pilot.

If you absolutely, positively must impose asymmetric loading on an airframe, you should not rely on a panel-mounted g-meter, which doesn’t record the maximum load a wing sustains. Instead, it only records loading on the panel-mounted g-meter. A good rule of thumb is to limit asymmetric loading to / of the airframe’s load limit, e.g., use 4g for an aerobatic 6g airplane.

https://www.aviationsafetymagazine.c...vering-stalls/

[44 AMP]

A point to consider, the scope landed on its front end. That means that the force applied to the internal mechanism was in the opposite direction than the force of recoil.

Many scopes are not made to take stress in the forward direction. More than a few have been killed by air rifles.

You have two choices, use the scope as is, and see how it behaves, or send it back to the maker for evaluation / repair.

[tangolima]

Here are the calculations I did.

1. g force of a .50 BMG rifle

Peak chamber pressure gives rise to instantaneous peak acceleration. Peak force on bullet is same as the peak force on rifle

F=(0.511/2)^2*pi*55e3=11.38e3 lbf

Peak acceleration

apkr = 11.28e3/(20/32.34) = 18.2e3 ft/s^2 or 563g

Average acceleration is much low but sustains over barrel time. Average acceleration of bullet

aavb = 2900^2/(2*45/12) = 1.12e6 ft/s^2

Average acceleration of rifle

aavr = 1.12e6 * (800/7000/20) = 6.4e3 ft/s^2 or 198g.

Barrel time

t = 2900/1.12e6 = 2.6ms

2. g force on scope when impacting floor.

No way to estimate peak acceleration. Average acceleration can be estimated by depth of dent and assumed impact duration.

Speed of scope hitting ground

Vs = sqrt(2*32.34*3) = 13.9 fps

The dent is about 0.125" deep. Average acceleration

aavs1 = 13.9^2/(2*0.125/12) = 9.3e3 ft/s^2 or 288g

Average acceleration assuming impact duration same as barrel time

aavs2 = 13.9/2.6e-3 = 5.3e3 ft/s^2 or 165g

3. Conclusion
Glass breaks around 10,000g. .50 BMG gives rise g force way below that.

The scope hits the ground at average g force similar to a .50 BMG. Glass didn't shattered. Reticle is etched on the lens, so it is ok.

Side load could have pinched the adjustment tube and changed zero. Probably, but no way to be sure. The scope fell off the rifle already. It seems working fine, minus the dent.

-TL


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[jmhyer]

Same thing happened to me about 15-20 years ago with a $200 Bushnell Elite scope in 3-9x40. It zeroed just fine and is still holdig strong all these years later.