If you had a compound bow and arrow, facing off against a single .38 caliber cartridge, what would be the relative distance between the launch of the arrow hitting a target with the same force as a .38 cartridge from an equivalent distance? Would the .38 cartridge be 200m away while the bow would be 80m? How would you figure that out? I know that the arrow has more weight, so more force. But the bullet has more velocity...How could I calculate the exact distance that would make both exert the same force on the same target. How far away would the bow and arrow be and how far away would the gun be?
Enjoy the benefits of a premium membership!
Upgrade Account
-
TalkBass has been independent since 1998. Add your voice.
Create a free account to reply to discussions, view embedded media, and browse with fewer display ads.
Join free Log in
Want zero display ads or expanded classifieds tools? Compare plans.
Physics Question
- Thread starter FingerDub
- Start date
the force you're talking about is inertia, and although a bullet is smaller, it's lead & it's traveling very fast
so just figure out the mass of each (in grams) & the velocity of each (in meters/sec)
so just figure out the mass of each (in grams) & the velocity of each (in meters/sec)
Once the initial force is calculated (mass * velocity), the force of aerodynamic drag will need to be known for each object. Using this, set the forces equal and solve for distance. This is still ignoring the acceleration of gravity. Is there an app for this?
Once an arrow is shot or a bullet is fired, they don't gain force by traveling more distance. They will have roughly the same force from a few feet away as a hundred feet away. They would lose some momentum from wind resistance, and gravity.
My gut says that a bullet will have more force, up to the point they both become inert.
My gut says that a bullet will have more force, up to the point they both become inert.
Force equals mass times acceleration, not velocity. The force distance would be the distance the projectile travels into the target. The acceleration would be calculated by change in velocity over time. Basically the velocity at the time the projectile impacts the target divided by the time it takes to slow to zero. The force slowing the bullet equals the force of the bullet hitting the target.
If you solve those for the same force value, you can figure out the velocity when the projectiles strike the target. The difficulty here is the distance is going to be a function of the initial velocity.
When you have the impact velocity for both, you just need to calculate the distance you would have to stand away until drag slowed the projectiles to the correct impact velocity.
Objects don't have force ever. They are acted on by force. A force causes an object to accelerate. That force is equal to the mass of the object being accelerated times the acceleration.
Jedis and the Sith do have the force within them, but that is an exception.
And what purpose would it serve to know these actual calculations?
The arriving settlers in the Americas came with guns, the natives had bows and arrows.
The settlers are still here in the millions and claim land from the Atlantic to the Pacific oceans.
Math/physics wouldn't have helped the American Indians, equal munitions might have.
The arriving settlers in the Americas came with guns, the natives had bows and arrows.
The settlers are still here in the millions and claim land from the Atlantic to the Pacific oceans.
Math/physics wouldn't have helped the American Indians, equal munitions might have.
Distance and force are not what you want here, I think. Momentum is mass * velocity, and that's what the target will "feel" when hit. So, if the arrow weighs 4 times as much, and travels at 1/4 the velocity of the bullet at the time of collision, they will have the same momentum.
The easier question is what distance would the two projectiles need to be fired to strike a target with the same energy. That would tell you when they would roughly deliver the same damage.
The primary energy to consider is kinetic energy which is proportional to (mass x velocity x velocity).
m1v1²=m2v2²
You could assume a bullet had a lot more kinetic energy when fired. So set v1 as the top velocity of the arrow at a distance of zero. So the only unknown is the velocity of the bullet v2.
v2=√(m1v1²/m2)
Then you need to calculate the distance the bullet will have to travel to slow to that velocity. Drag is the complicated part.
If you can estimate drag in a linear fashion or find an online calculator, it will be your best bet. But with that you would know the distance.
Last edited:
The target will feel the energy which is proportional to velocity squared. Energy is more important than momentum. Energy is really what gets transferred. So in your example, the target hit by the bullet will feel 4x the energy.
1 x 4² = 16
4 x 1² = 4
Last edited:
The 1/2 cancels out when just comparing one kinetic energy to another. I left it out for simplicity since none of the numbers have any units anyway. Still 4x the energy.
Is... is anyone going to ask why we're comparing these projectiles? I feel like we're missing a really good story here.
--^@
--^@
you want a joules calculator.
Airsoft-FPS/ Joules Calculator-Shipping Policies
enter the weight of the projectile.. and the speed in feet per second, and you will get a result measured in Joules.
Airsoft-FPS/ Joules Calculator-Shipping Policies
enter the weight of the projectile.. and the speed in feet per second, and you will get a result measured in Joules.
