KE = 1/2 mv^2

[AustinL911]

As I'm sitting here working on my pre-course modules for TNCC (Trauma Nurse Core Curriculum [I'm an ICU nurse at a Level-1 trauma center]), I've happened upon this physics formula again. I've never really thought much about it until now, but it made me think of archery. In dealing with traumatically injured patients, we tend to think about energy transfer a bit and how it relates to their injuries.

The basic premise is this: if you doubt the mass of the object that hit the patient/animal (car/arrow), the KE is doubled. However, if you double the velocity of the object that hits the patient/animal (car/arrow), KE is quadrupled.

If that's the case, why do so many, including myself, choose mass > velocity when selecting an arrow? Inertia? Momentum?

It seems to me that velocity (pending the arrow stays intact) buys you more for your money.

Thoughts?

 

[IdahoBeav]

Momentum (p=mv) is a much better means of determining which mass and velocity combo will produce greater penetration.

Even if using the KE equation, we must remember that mass is conserved but velocity is not. This is why many people will still go with the heavier arrow and sacrifice speed while considering KE.

In my opinion KE is a number the Archery industry uses to sell new equipment.

Sent from my SM-G950U using Tapatalk

 

[awaldro7]

I have had this dilemma before also and I think that part of the problem is that its a lot easier to increase the mass than the velocity by the same percentage. You can increase an arrow by 50% from 350 gr to 525 gr easier than you can make a 300 fps bow shoot 450 fps.

 

[Screamrider]

Broken down to what really matters.....arrows kill by penetration, not kinetic energy (which does play a far more significant role with bullets).

The real juice for penetration is momentum, not KE. Since KE squares velocity in the equation, it heavily biases a faster arrow. The momentum equation is simply the product of velocity and mass, so both parameters have equal impact in the equation. The analogy I like best is what would you rather be hit with: a 2 ounce tennis ball travelling at 100 mph or a 6 lb (96 ounce) bowling ball travelling at 15mph - both have almost the same KE, but the bowling ball has over seven times the momentum compared to the tennis ball. An extreme example I know, but it highlights the value of momentum over KE.

Any 3D course is also a great case study. Just yesterday I shot a tournament with a buddy and we had almost identical set-ups. We even had the same arrows, only mine were 455 grains vs his at 380 grains (I use brass inserts, additional screw in weights and 125 grain tips). Even though his arrow were travelling at significantly greater velocity, just try pulling the 2 arrows from the foam and you quickly see which penetrates deeper.

 

[roadrunner]

KE is merely the representation of the work required by the bow to move the weight of the arrow, m, at a certain speed, v. Velocity is dependent on the arrow's weight.

Because the relationship is directly proportional between weight and velocity, if momentum goes up, so does KE. More energy used to get the mass moving also means more will be used up later. In the case of archery, you do not want an elastic collision (otherwise your arrow would bounce off the target).

There is a happy medium to both weight and speed and a wide range of combinations that will yield the same result.

I prefer an arrow that weighs 400 grs (+/- 10) and a speed of 300 fps (+/- 5 fps).

 

[mfllood3800]

I have been under the guidance that speed and KE are important, but what is key is the resistance of the object absorbing the impact. Meaning what keeps moving at its greatest momentum and fights resistance of the object the best.
I read on this years ago when all the debates were high and opinions fresh.

Therefore I choose skinny arrows, with heavier over all weight, while maintaining good speed with a bit more weight up front for keeping that momentum moving thru the resistance of the muscle matter.

Many opinions on this, but in the end, any set up can be lethal.

I have shot thru cow elk at 82 yards with a 300 gr arrow shooting at 340 fps
I have shot thru Bull elk, with a 472 gr arrow at 300 fps
I have shot thru deer at 70+ yards with set ups in between

The only consistent in these variable instances, was my broad head. It is the one with best ability to resist resistance.

 

[roadrunner]

A tennis ball flying at 100 mph will hurt [and kill] just as effectively, so I guess it doesn't matter in the end.

For any math/physics nerds, KE is the area under a momentum curve from t =0 to t=n (point of impact) and is a scaler quantity. Pretty much meaningless really...

 

[tipsntails7]

As I'm sitting here working on my pre-course modules for TNCC (Trauma Nurse Core Curriculum [I'm an ICU nurse at a Level-1 trauma center]), I've happened upon this physics formula again. I've never really thought much about it until now, but it made me think of archery. In dealing with traumatically injured patients, we tend to think about energy transfer a bit and how it relates to their injuries.

The basic premise is this: if you doubt the mass of the object that hit the patient/animal (car/arrow), the KE is doubled. However, if you double the velocity of the object that hits the patient/animal (car/arrow), KE is quadrupled.

If that's the case, why do so many, including myself, choose mass > velocity when selecting an arrow? Inertia? Momentum?

It seems to me that velocity (pending the arrow stays intact) buys you more for your money.

Thoughts?

Its already been stated but momentum is a better determiner for Penetration.

if a car hits me, I am not entirely worried about penetration, as that is most likely not going to kill me, the KE of getting hit by a car will. again this is a basic analogy and is not true of every instance.

Archery kills by blood loss (for the most part) in order for that to happen the arrow needs to maintain its path of travel through the animal. KE is a non directional form of energy, so think of it as a shockwave that happens the moment it hits the animal. give an animal a big enough shockwave and it can kill it (IE person being hit by a car).

 

[ghost338]

Good responses here. Not much to add. Practically speaking, you want to shoot a combination of weight and velocity that maximizes your momentum, which was already mentioned.

I'll add that mathematically speaking, if you use the impulse theory, you could calculate a relative theoretical penetration depth between different combinations.