# The physics of flying archers

A kind of soldiers in my world can use certain magical equipment to launch themselves into the air and stay airborne (sort of like gliders. They need to keep moving ahead; they can't hover much). Note that they need to keep their hands free whenever possible; they use magical gloves on their hands (and feet, but they're not very useful once airborne) as sort of close range grappling hooks cum vacuum pads which can be used to propel them at no damage to themselves due to the magic (but a lot of damage to whatever they used to propel themselves)

While there are many ways I've thought of in which they use throwing knives, lances, swords etc. while airborne, is it possible to use bows or crossbows?

1. Is it possible to draw a bow midair? If not, then they would use crossbows that they would load while on the ground and shoot once midair.
2. Once the arrow is released, how would conservation of momentum affect them? If they shot in front, it would send them flying back, or at least slow down their forward movement a lot, maybe forcing them to get down to where they can use the ground to propel themselves. If they released it downwards, while flying above the enemy, would it propel them upwards? Does an arrow have enough momentum to do any of these?

Is this even effective at all? Or would it be better to give these archers closer range weapons and send them into the fray? Because these are some elite military units, used for some of the most difficult tasks or for stuff like horseback chases. So would it even make sense to train some of them for ranged combat?

• i believe crossbow is possible, and the way you describe it is fine to use strong crossbow, though you mention they need to keep moving which may disturb their aim though if you want precise shoot, but iam not sure about bow though especially after you shoot it (by standing posture) if you dont have good foundation or stance, unless they use weaker bow, maybe not much if they are laying down gliding, i think. Jan 19 at 7:36
• Fighter planes have guns. It is possible to fire mass forwards of the aircraft without significantly affecting its trajectory. This works because, as fast as a bullet fires, it weighs far less than a plane. Arrows don't fly nearly as fast, so the amount of kickback on the flying archer would be similarly negligible. Jan 19 at 15:42
• @DarrelHoffman Some planes with very heavy guns are designed so that the firing barrel is along the centerline of the plane. Otherwise, firing the gun would cause the plane to twist and ruin the pilot's accuracy. A small change in heading isn't quite the same as stopping the forward momentum of plane wholesale, but it can be a non-negligible design consideration if you fire bullets that are big enough fast enough. Jan 19 at 16:46
• Accuracy is going to be the real issue. This is at least as difficult as shooting from a moving horse, and that takes years (usually starting in childhood) to learn to do that with any accuracy and competence (e.g., not dropping your arrows, or bow, etc.). Jan 19 at 18:04
• lo an behold the mighty A-10 where the gun provides as much thrust as one engine: aviation.stackexchange.com/questions/39511/… Jan 19 at 22:08

### Yes you can, and a subtle effect.

Rather than getting all physics on you, I'd suggest the best way to understand this is to try it: hop on a skate board / roller skates / frozen lake / floor covered with lube, put on some safety gear like helmet, and give this a shot, the physics are the same. (It's both fun and educational!).

1. Assuming you're able to fly with your hands and arms free enough, then yes, you can draw a bow while airborne.
• At the risk of my technique being ripped into by the expert archers, basically you're pushing the bow with one hand and pulling the string with the other, and the difference between those forces will draw the bow by deforming it. There will be no net acceleration on you when you do this assuming your travelling at safe speeds (eg <100km/h) and wind drag isnt that much of an issue.
2. There will be subtle recoil acceleration from releasing the bow. Not enough to knock you out of the sky.
• This is known as conservation of momentum.
• Assuming 100kg flyer, 10g arrow, and 100m/s (360km/h) launch speed. Your arrow will impart 1kgm/s of backwards momentum (10g * 100m/s), you will decelerate by 0.01m/s (0.036km/h) 1kgm/s / 100kg.
• If you were travelling at 10m/s (36km/h), you'd need to fire ~1000 arrows before you come to a complete standstill.
• I'm not an expert archer but I mostly agree with what you said. At first I found the part about difference between the forces confusing but indeed, subtracting a vector from its opposite is the same as doubling it. The way it works though is that you bend the bow's arms backwards - they store energy in the deformation. When you release the string the arms go back to their neutral shape and the energy is put on the arrow. Regardless of the string, you get different results with different arm materials and shapes - even using the same force! Jan 19 at 10:24
• Adding to what I said above about materials - in practice though the important difference between any two materials is usually the force needed to bend them - and the more force you need, the more energy the arms can store for the same deformation. Jan 19 at 10:40
• Good answer. If you're doing order of magnitude estimation, I'd recommend bumping the launch speed of the arrow by an order of magnitude. Modern compound bows can exceed 100 m/s arrow speed. Jan 19 at 15:38
• Of course, if you start with 1000+ arrows in your quiver, your quiver weighs more than you, so you can't neglect quiver weight in initial conservation of momentum calculations.
– Sam
Jan 19 at 16:11
• If the quiver weight becomes significant, you may need to apply the rocket equation. Jan 19 at 21:43

Drawing a bow midair doesn't look impossible, and seems way more practical than bringing loaded crossbows along. Due to practical limitations, how many crossbows could one take along? 5 seems to be already a large number, and a flying attacker firing up to 5 darts before stopping seems rather underpowered.

Also recoil doesn't seem to be a huge issue: first of all the departure speed of an arrow is way lower than the bullet coming out of a gun/rifle, and so is its mass.

If you take an arrow leaving the bow at 100 m/s (which is about the fastest arrow a composite bow can launch) and with a mass of about 50 grams, it would rob an archer weighing 70 kg of just $$100 \cdot 0.05 \over 70 =0.07 \ m/s$$ of velocity.

The above follows from the conservation of momentum $$m_1 \Delta v_1 = m_2\Delta v_2$$

• A lot of widely used rounds for modern firearms actually use bullets that weigh less than most arrows. Typically used arrows in modern times weight around 420-500 grains, while a lot of ammunition used with modern firearms of a caliber smaller than about 12.7mm is in the range of 90-200 grains in terms of weight. The speed difference is where most of the energy difference arises, most arrows fired from modern bows are moving at just over one-third of Mach 1 as they leave the bow, while most bullets are moving at least twice as fast. Jan 19 at 18:28
• @AustinHemmelgarn -- I'd argue more than 3 times as fast -- subsonic ammo is something you have to specifically ask for in most calibers (some larger handgun calibers start off subsonic, but that's not common) Jan 20 at 1:32
• @Shalvenay It really depends on the caliber. Some larger handgun calibers are indeed normally subsonic, but so are some smaller ones (.32 ACP and .25 ACP for example), and there are plenty of standard-subsonic or readily subsonic rifle rounds (.300 BLK for example was designed specifically to be subsonic (though many loads today are at least transsonic or even supersonic)). Jan 20 at 2:24
• @AustinHemmelgarn -- kind of forgot about .32/.25 ACP and .300 BLK, yes Jan 20 at 2:27
• Also: you can probably get away with smaller/lighter arrows since they actually will GAIN speed after being fired due to gravity. Meaning that you need to put less impulse (aka less recoil for you) into them to have the same end impact Jan 20 at 11:56

Lars Andersen can catch an arrow shot at him and accurately return fire while still in the air. It is by no means impossible to shoot a bow while in the air.

Conservation of momentum means that the momentum of your projectile will be subtracted from the momentum of your archer once it is fired, according to the law. A heavy arrow might weigh as many as 40 grams (600 grain), and could be shot as fast as 150 kph. The total momentum would be 0.600 kg*km/h. You then divide that momentum by the mass of your archer in kilograms, and that is how much they have slowed down. A 50 kg archer would be slowed down by 0.012 km/h, or would have to shoot about 83 arrows to be slowed by 1 km/h.

I would expect the tactics used to be similar to and just as effective as Mongol horse archery.

• Keep in mind that Lars Andersen use low poundage bows, and often don't do a full draw. War bows require much more force (and therefore also time) to draw. Jan 19 at 10:47
• That is a good point. Since he uses a Eastern-style light bow, his arrows may not penetrate heavy armor. However, his arrows can penetrate light chain mail, so lightly armored and unarmored opponents would still be susceptible. Additionally, in the question's scenario, the archers' fall is slowed by magic, giving them more time in the air to shoot. Jan 19 at 19:12
• @Jafego, according to other reconstructions I've seen there is a massive difference in how the chain mail is made in whether it can be penetrated. If the wire is just bent into a ring but left open, as is the case with any replica made for show, it is penetrated easily even with light bow like this. But a real mail was riveted, the ends of each ring carefully joined together with a tiny rivet. It was a lot of work to make, but then even a 160 pound bow needs a very good hit to penetrate it. Jan 19 at 22:05
• @Keptox, however, here we have arrows falling down. Aka they accelerate more after being fired (or at least cancel out air drag to some extend), how relevant that is obviously depends on the height of the airborne troops (and at some point just dropping flechettes becomes the better option), as well as the desired tactic (sniping individuals vs suppressive fire) Jan 20 at 11:59

Throwing and drawing a bow require a remarkable amount of core and upper body movement. Throwing specifically is the art of transferring the momentum of your body into another smaller object.

I have some practical experiments for you. Throw a ball normally to judge your range. Throw a ball while sitting down. Throw a ball with your back to a wall.

Now consider that required body movement, the body movement for drawing a bow is similar to that of winding up a throw, and how your soldiers control their gliders and their body position while using the glider.

Consider along with this the way an arrow lies on a bow, it's not constrained by much other than gravity. Which side it lies on depends on the type of bow they use and the style of release (normally left side for right handed).

This will give you the practical angles at which a bow could be fired effectively while using the glider, however throwing while gliding likely lacks the body control and stability required for significant power transfer and you'll be better of dropping objects from height rather than attempting to throw anything.

Is it possible to draw a bow midair? If not, then they would use crossbows that they would load while on the ground and shoot once midair.

I went to a martial arts school with an archery range. One of the things the instructors had us do for us to learn how to shoot fast was leaping over a bench or a chair (while running) - and we had the time in the air to aim and shoot. Most of us did start the jump with the arrow already nocked, but some of my most graduated colleagues managed to nock the arrow mid-jump.

For conservation of momentum, see the other answers for the math. But for simplicity, many archery range targets are lighter than an adult and are not knocked down by the arrows that hit and get stuck on them. An arrow won't change an adult's momentum much.

All these answers are neglecting the boring realities of the effects of these archers on "real combat".

There are two aspects to a projectile's range and terminal velocity:

• Initial launch speed
• Initial altitude

Fighter jet pilots know this well - the main complaint about the F-35 is that it will launch a missile from lower altitude and with less velocity than its competitors, therefore the enemy will "dump on it" and get out before the F-35 can respond.

You have a similar situation - your magic archers will impart forward velocity just before firing, and they will do so from altitude.

The result? Terminal velocity on impact, from outside of the enemy's engagement envelope.

Basically, you just invented an undefeatable force, for conventional armies. Invest in big shields and SOF* to attack re-supply stations and ambush resting archers.

With all that said, do you really need "archers"? What keeps you from having flying dudes who just toss bags filled with pointy rocks from altitude? Put them on a disk that spins and throws them in random directions at x altitude via spring. You basically just invented medieval air burst munitions. Your "archers" aren't going to be firing at point targets anyway.

Oh, and say goodbye to normal fortifications. Have fun with this rabbit hole, it never ends.

Edit based on reply: In that case, the "real world" application is signaling. Look up "indirect fire grids", "designated kill zones", etc. The really simple version of this is that the commander pre-defines squares within range of his artillery, kind of like on a chess board. Your "archers" fly around and look if the enemy is advancing on any of these squares, and then give a signal to your catapults for indirect fire on these positions. Anyway, this is only if you want to get fancy with "practical applications. You could have them zooming around and firing on generals / mages / whatever. Probably in low-visibility conditions - at night, in fog, etc.

*Special Operations Forces

• +1 however these are elite soldiers too few in number to cause significant tactical changes in the enemy army, moreso used for difficult tasks or taking out specifically magically superpowered enemies than in conventional warfare (again, too few) Jan 20 at 5:01
• What do you mean by SoF? Jan 20 at 5:01

Why bother with bows and arrows at all? They could just drop or throw air-based flechettes.

The flechettes have a higher terminal velocity than arrows and gain kinetic energy as they drop. Also, flechettes (as well as arrows) benefit from the initial velocity of the weapons platform. A two-inch long version of these weighing only 0.7 ounces called the Lazy Dog was used to devastating effect in Vietnam and

could be hurled from buckets, dropped by hand, or thrown in their small shipping bags made of paper

A satchel of these bad boys would allow a flying human to devastate ground troops.

• They aren't going to be fighting ground 'troops', as in formation, as much as irregulars and special engagements. They are less bombers and more sharpshooters. Archers are just a subset; many of these soldiers go forward and engage enemies using small knives, short sword, rope darts and a long lance-like weapon great at harassing from outside melee distance. Their method of flying, essentially grapplining through the air using magical hand and feet pads and a healthy dose of air magic to provide a bit more lift, is itself a weapon: They can 'push' against an enemy's head: it would explode Jan 20 at 19:12
• However those are more or less close range fighting techniques. Archers here are being used to precisely take out targets long-distance. They can sometimes help regular forces too - they are still trained archers (for years), who can also jump very high to take potshots at enemies out of reach. It would be highly impractical to just throw a heavy projectile at the enemy from such a distance. That is a job for the close range engagers, who DO use such techniques often (though they typically favor knives over blunt projectiles - it can be used as the former but also as a knife Jan 20 at 19:16

It strikes me as slightly odd that you are worrying about real physics when you've already got the archers doing 'flying by magic'... why worry about conservation of momentum or the like in this circumstance? You could just define that they are able to operate whatever weapon and that it has no effect on their velocity or height as it's compensated for by the magic.

On a more real physics not, drawing a bow / crossbow requires the archer to act against their own body to store energy in the bowspring. From a physics point of view, it's all in the archer's frame of reference so what the archer is doing in an external reference frame shouldn't matter... up to the point they loose or launch or let fly.