## Thursday, April 8, 2010

### Would a laser gun recoil?

Today I'd like to approach a question near and dear to many a geek heart: do laser guns have recoil?

Let's motivate our question a little bit.  I've wondered about this question since I saw star wars.  Though I'm no firearms expert, the recoil in guns must come from conservation of momentum principles. Momentum is conserved in a system. The gun starts with zero momentum. We fire, give the bullet momentum, and so to keep the system at zero momentum, the gun must gain equal and opposite momentum. That is, the gun will move backwards.

All of that was for conventional guns. Light carries momentum, so if we fire a pulse of light, we expect our laser gun to recoil. So yes, they do have recoil. Satisfied, dear readers? Neither am I. The question we really mean to ask is, does a laser gun have noticeable recoil?

We need to make a few reasonable assumptions. Let's assume that the laser gun fires a pulse with as much energy as a bullet has kinetic energy, KE. The energy, E, of light is related to its momentum, p, by E=pc, where c is the speed of light. This gives a momentum of

$E=KE=pc$
$p=\frac{KE}{c}$

What is the kinetic energy of a bullet? A little searching reveals that a .22 bullet is ~2.5g and fires with a muzzle velocity of ~330m/s. Kinetic energy is given by KE=1/2mv^2, where m is mass and v velocity. So, the momentum of a laser pulse with equal energy would be

$p=\frac{mv^2}{2c}$
$p=\frac{.0025kg*(330m/s)^2}{2*3\cdot 10^8m/s}$
$p=4.5\cdot10^{-7}kg \cdot m/s$

For comparison, the momentum (p=mv) of a .22 bullet is .83 kg*m/s. The momentum of a laser gun is 2 million times less than the momentum of a .22. But is momentum all we should consider?  I suspect the 'kick' we feel on the recoil is directly related to the force that the gun exerts on the holder.  This means that instead of momentum we need to consider impulse, momentum per time.  We estimate the time it takes to fire a .22 is ~.1s, so the force delivered 8.3 N.

Let's estimate the time it takes a laser gun to fire.  Unfortunately, not having a laser gun to fire (feel free to send me one, dear readers), we're more or less going to have to guess at the firing time.  Most movies with laser guns show pulses of light (which, incidentally would move so fast we wouldn't see them) on the order of a meter or two long.  Given the speed of light, this would give a firing time of ~30 nanoseconds.  This would give a force delivered of 15 N.  This is close to what we estimated or a .22.  So, if movies are to be believed (and really, why wouldn't we believe them?), it seems like laser guns may well have recoil.

Note:  It is worth questioning if we need the same energy for a laser as for a bullet.  That could certainly change our estimate.  Maybe we'll return to this question again.

1. But a force of 15N applied for 30ns would hardly be noticed by the user.

2. Isn't 30ns about 30 light feet or maybe 8 meters, not one or two meters. The first Star Wars movies actually had shorter pulses, maybe a foot or two long.

3. Kaleberg:
You're absolutely right, 30ns gives 9m. As for the pulses . . . I actually did a little research (I'm such a geek!), the hand held blasters in the star wars movies don't shot light, they shoot some kind of directed plasma. Only the starships shoot actual laser beams (along with some of the defensive emplacements, like on Hoth). I don't know the size of the starships, but 10m seemed about right. As the image above shows, the lasers from ships were on the order of the ship size! That's the long answer. I did so much research both for fun, and because I figured someone would call me on the hand-held blasters otherwise.

Devin,
I've really got no idea how you would feel a force applied over such a short time scale. It's completely out of my realm of experience! You could well be right. I'll let you know when I find out ;)

4. I always assumed (because it was convenient to me) that the cannons expelled massy particles and then propelled/continued to elevate their energy level by way of laser. This also allows Star Wars fans to overcome the standard Star Trek defense that craft in Star Trek have mirrored hulls and thus deflect lasers.

Of course, this creates a requirement that the bore-sighted laser stays perfectly aligned as the gun carriage recoils, less it cause the massive slug to dissipate.

5. "less"="lest"

6. Nato,
I did a little research on this. Not much. What I determined is that it looks like the hand-held guns expel massive particles, while the ship-to-ship weaponry is actually laser beams. Of course, I make no claim to be an expert in this area.

7. calculate how far the gun would hve accelerated (s = 1/2at^2) for the duration. this should give a better indication of how noticeable the recoil is

8. An interesting idea. We'll use Matt's estimate of 5kg for our laser gun mass. This would give a distance traveled of
$d=\frac{15N(30ns)^2}{2(5kg)}=1.35\cdot 10^{-15}m$

This is a miniscule distance (about a nuclear diameter), so if this estimate is correct, we would certainly not notice the recoil.

9. addtionally a laser is very very hot so when you shoot your laser gun the air at muzzle break will also get very very hot so the expanse of air could also give the appearance and feel of recoil

10. I've done some research on realistic man-portable laser weapons and photon rockets. A photon rocket is a rocket whose propellant is photons- light. They have the highest possible exhaust velocity, so they have a very high specific impulse. Specific impulse is the measure of how much change in velocity a rocket gets for every gram of propellant it uses. Since light carries momentum, photon rockets and light sails work. A spaceship can be propelled by light. However, thrust is very low. To obtain one newton of thrust, a photon rocket would need to output 300 freaking megawatts!! The spacecraft would be spewing out a freaking super laser beam and riding the recoil. We don't have such rockets today- for obvious reasons. You could make nuclear fission powered photon rocket, but the thrust would be so miniscule you would not notice it. You might sit around for years in orbit before you even notice a change in your speed. Obviously, there is no way a handheld laser gun would ever output enough power to have noticeable. Ever.

Real man portable laser weapons won't resemble star wars blasters. The gun will have a lens or mirror in the beam emitter- probably several centimeters across to avoid being damaged by the super- intense light. The heat from the beam will cause the water in flesh to bloom explosively into steam, ripping flesh apart and causing third and second degree burns over much of the surrounding tissue. A pulsed laser action would allow the laser to drill deeply and reach vital organs. A variant in which several beams were fired slightly off- axis of each other would leave a wound much like a knife wound, or possibly cut a human in half. No laser will have noticeable recoil. Lasers move at lightspeed and strike instantly. In a vacuum, lasers are invisible. In air, the beam might leave a visible trail due to atmosphere induced scatter, ionization, and bits of debris burning under the irradiation of the beam.

-Cristopher Phoenix

11. I am learning about all sorts of waves now in physics 3, including electromagnetic waves and one of my homework questions is whether or not someone who turns on a flashlight experiences recoil due to the light having momentum and why it is not observed. It would make sense for light to cause a recoil because one knows light has a speed and would therefore have a momentum and with a momentum, p=mv^2 proves it has a mass.

However, in my opinion, as counter intuitive as it may seem, I believe light, and laser beams in that extent, do not cause recoil. Light is composed of photons, which according to modern physics have no mass. This is because the modern definition of mass depends on the object in question at rest and photons are never at rest and therefore, never have mass (mind boggling for me).

I am a chemist undergraduate and I do research and experiments with lasers and I know that a laser primarily heats up materials due to excitation of the molecules and breaking down of bonds. This is caused by the nature of the wavelength of lasers. A neat trick is that if you are working with a laser, lets say a red one, and you have a red shirt of the exact same wavelength, then it will not burn. Any other color would become singed almost immediately (depending on the wavelength of light versus shirt and its strength).

Hence, assuming modern physics is correct, photons have no mass and therefore, no momentum, but they do have velocity, which allows them to move through mediums. As well, they react with their environment due to their wavelength. So, a laser gun would likely have no recoil. Unless of course I have some sort of flaw in my logic, which I most likely do.

-Johnny boy

12. Johnny,

Here's the issue with what you said. While it is true that if something has mass and velocity it has momentum, the converse is not true. That is, if something has momentum, it is not required to have mass and velocity. Photons are proof of that. We've shown this experimentally (we being the general physics community).

However, the momentum of light is quite small (as I mention in the post), so that is why we don't tend to notice it.

13. By my reckoning, you divided by two where it was not necessary:

.5(m1)(v1)(v1) = KE = .5(m2)(v2)(v2)

p2 = (m2)(v2)

p2 = KE2/v2/.5

p2 = .5(m2)(v2)(v2)/(v2)/.5

Or

p2 = KE1/v2/.5

p2 = .5(m1)(v1)(v1)/(v2)/.5

Cancel

p2 = m1(v1)(v1)/v2

In other words, you're off by a factor of two.

Also, you should probably consider that the bullet continues to accelerate even after it exits the barrel of the gun (this varies in distance), which means variable impulse.

14. Am I the only one who objects with using a 2.5g .22 at 330m/s, when a 9.7g 7.62x51 at 850m/s would be more suitable?

.22 is a varmint round, noone walks into combat with that caliber if they can help it. 7.62 is considered a full power combat round.

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16. The equation seems to be very difficult for a layman

17. Just one thing: unless I am mistaken, blasters in the Star Wars universe don't fire lasers at all -- they're actually (well, supposedly) firing clumps of charged gas or something like that. Ergo, you get your recoil.

My source is The Star Wars Sourcebook, published by West End Games in 1987. I'll verify that once I am able, but if someone beats me to it...