Wind needed to deflect a bullet

Question

In a world with magic, bullets pose a serious threat to magic users. I had an idea for a spell that would use wind to stop/deflect/slow a bullet to make it harmless and thus have magic be more effective than the use of bullets. How fast would the wind have to be to deflect a bullet? Also the mages are immune to the effect of their own spells so they will not get blown away by their spell.

Edit: The bullet is from the standard sniper instead of a glock and the distance is from 105 meters.

Answer 1

I was a bit slow in answering this, but lets take it that the wind mage has some sort of "passive and automatic wind barrier" that isn't effected by the reaction speed of the caster. This seems to have two similar yet different problems in it. Can you slow/stop a bullet, and can you deflect a bullet? Lets look at these separately.

Slowing / Stopping

This problem is all in one straight line, so if we can keep the velocities and accelerations straight, the numbers shouldn't need any calculus. I'll be assuming we're working with a 9mm handgun.

If a wind mage casts a spell at 100 meters directly at the gunman, who has perfect aim, then what kind of wind will be needed to stop the bullet in time?

$force_{wind} = \frac{1}{2} density_{air}*(v_{muzzle}+v_{wind})^2*coef_{drag}*crosssection$

$force_{wind} = m_{bullet}*a_{wind}$

$v_f^2 = v_i^2 + 2a_ {wind}d $

We know roughly that $density_{air} = 1.20458\frac{kg}{m^3}$ , the muzzle velocity of a 9mm is $1200\frac{f}{s} \approx 366\frac{m}{s}$ , the distance between the mage and gun is $100$ meters, the 9mm has a diameter of $9mm$ , which is a cross section of $\frac{9^2\pi} {4}mm ^2$ and that a head on bullet has a drag coefficient of $0.38$ .

Plugging that all in and chugging through, we get $219\frac{m}{s}$ , or $491mph$ . Going by this scale by the National Hurricane Center , 500 mph would make a Category 5 Hurricane look cute, destroying anything in it's path.

Deflecting

This is a different problem, all we need to do is nudge the bullet over by half the width of a human before it gets there.

I'm going to simplify this problem like this: The bullet will travel without air resistance in a perfectly straight line until all the wind acts on it at the same time. This lets us work with triangles instead of curved paths.

The angle of deflection from the bullet to the person to miss is $arctan(\text{The width of the person} / \text{The distance to the person})$

We also know it in terms of velocity $arctan(\text{The speed tangentially away from the person} / \text{The speed towards the person})$

The speed tangentially away from the person, like before is

$force_{wind} = \frac{1}{2} density_{air}*v_{wind}^2*coef_{drag}*crosssection$

$force_{wind} = m_{bullet}*a_{wind}$

But in this case, the wind is acting on the side of the bullet, so the drag is $0.82$ and the cross section is $9mm * 19mm = 171mm^2$ .

$force_{wind} = v_{wind}^2 * 84\mu N$

$a_{wind} = v_{wind}^2 * 0.0113\frac{m}{s^2}$

And our final equation

$\text{human width}/ (\text{total distance} - t*muzzlevelocity) = t *a_{wind} / muzzlevelocity$

$465mm / (100m - t*muzzlevelocity) = t*a_{wind} / muzzlevelocity$

This leads to a quadratic in terms of a_{wind}. We only really need the discriminant to find what the minumum speed of the wind would deflect the bullet, and it's $47\frac{m}{s}$ , or about $104mph$ .

In conclusion, the best defense is a good offense, and if you can already apply hurricane force winds in the direction of a target, as g s pointed out, you probably have better options at that point than trying to blow the bullet out of the air.

Answer 2

Stop or adequately slow the bullet: not going to happen. The bullet is already going many times faster than a hurricane wind, it won't notice the difference over a short distance like 100m.

Deflect the bullet: maybe, depending on how super your superpowers are, but if you have the power to deflect a bullet at 100m, you're better off just knocking down the shooter.

Note that rifle bullets travel faster than the speed of sound, and will cross a 100m distance in about a tenth of a second. You can't react to the shot once it's been fired. Deflection must be pre-emptive. If you have to react to the shot, you're getting shot.

To accomplish the maximum deflection, you must apply the force over the maximum path length and at the maximum angle to the path. If you can only make winds go radially out from your body, you're getting shot.

Here's a fairly typical sniper rifle cartridge, courtesy of rifleshootermag.com.

We want the column for 100 yards. A yard is about the same as a meter. You'll notice that it only goes to 30mph - a very forceful, but not likely damaging, wind - and at that distance the maximum deflection from a 90 degree crosswind is 3 inches (7.62 centimeters, coincidentally). If you're unable to apply the crosswind across the whole length of the 100m gap, at much more than 30 miles per hour, you're getting shot.

We can see that the deflection distance varies roughly linearly with wind speed at all distances, so we can project that up to a wind speed big enough to make the bullet miss you: about 100 miles per hour (a powerful gust in a hurricane) across the whole distance between you and the shooter should move the bullet about 10 inches (25 cm) - enough to just barely save you, if the shooter was aiming for your center of mass.

However, the shooter can still hit you - either by random luck, having aimed slightly incorrectly, or by having learned the same table, and corrected ten inches the other direction.

On the other hand, you only have to move the gun a few millimeters to knock his aim off. Hit the shooter with some random strong gusts, and you'll be fine unless you have very bad luck.

Answer 3

Just about any wind speed will start to deflect a bullet, especially for a long-range, sniper shot.

Snipers are trained to correct for wind deflection by estimating wind speed and by shifting their aim. This is where magic comes in. Say you have a strong, localized wind around the mage, but it does not sway the nearby trees. There is no way for the sniper to estimate the wind direction.

The problem is that such a deflection works best if the bullet has a long way to travel after the wind hits it. If the wind is just a few meters from the mage, the bullet might turn a little, but soon thereafter it hits.

105 meters are not very long for a sniper shot.

Answer 4

Tornadoes are more than just wind

Effects on the bullet

Wind alone makes a pathetic bullet shield, but much like with your other question about weaponized wind, it comes down to what you have in the air. If you were to wrap yourself in 135mph tornado speed winds in a sandy or dusty environment, it would fill the air with a cloud of sand that is ~13.5 g/cuft. A standard sniper rifle fires a ~5g slug with a cross section of about ~0.1 sqin. This means that in order for it to fly through a 15 meter tornado, it will impact a total of about 5 grams of sand along the way which should be enough to significantly slow down and/or break up the bullet.

So, it's not so much the force of the wind that saves you here as it is the wall of solid matter it can hold up between you and the shooter. And this just assumes fine dust and sand in the wind, if the bullet hits something like a fence post, small rock, or some other significant solid object, it could completely stop the bullet. Whereas other answers that rely on pure air resistance can only barely deflect a bullet using the whole 100m, this solution allows you to form a much tighter shield around the caster.

Effects on Line-of-sight

Moreover, tornadoes occlude vision. Even though the air itself is invisible, all that dust and debris they pick up makes tornadoes opaque. So even if the bullet could reach you, the shooter may not be able to see where he needs to shoot.

Another option if you have other kinds of control over the air could be to summon a fog cloud. This would give you a much less destructive way to shut down snippers, and it also works really good at blocking Infrared, not just visible light. If you force gunmen to fight you in a thick fog, but your mages are "immune to the effect of their own spells", then your mages can see and eliminate gunmen before the gunmen can get close enough to know where to shoot.

Effects on the shooter himself

Another good way to stop a bullet with wind is to actually keep the shooter from aiming. At ground level, tornadoes have a much larger secondary cyclone around the main funnel. At 100m, the shooter might be outside of the fatal tornado speed winds, but he will still experience significant winds that will make holding his gun steady very hard. The difference of just 0.016 degrees is enough to change where your bullet lands by an inch. So, creating turbulent conditions that cause a sniper to sway by just 1 degree is enough to make him miss his mark by over 5ft... and this is assuming the sniper has protective eyewear, because that close to a tornado, he's likely to get a lot of sand in the face too.

Answer 5

While a super-powerful wind stong enough to curve bullets would be impressive, it would also be devastating as a weapon in its own right. The mage would be able to launch a hailstorm of rocks simply by casting the spell on a gravel road (bypassing your anti spell clause) or tear apart buildings like a walking tornado.

A spell which suppresses fire seems much more effective and would not require an easily circumvented anti-magic clause. Your mage glances toward the hill where the sniper is hiding and every candle, campfire, and cigarette on the hill is snuffed out. While the spell is in effect, guns in the spell area of effect are useless.