Spin Drift

[rsterne]

I did a bit of digging about "spin drift" today.... It is a sideways drift caused by the bullet spinning, in reaction to the downwards force of gravity, being resisted by the gyroscopic stability of the bullet.... This causes the bullet to yaw.... It is dependent on several factors, and occurs even in NO wind.... Bear in mind all this theory is for BULLETS....

It is to the right for a right hand twist (the most common) and to the left for a left hand twist.... Some claim that for pellet this is reversed....

The lower the velocity, and the longer the range, the greater it is, because it depends on the time of flight (raised to the power of 1.83) which means roughly the distance squared.... A higher BC means a higher AVERAGE velocity to the target, so a shorter ToF, for a given MV….

The faster the bullet is spinning (for a given bullet), the greater it is, because it depends on the gyroscopic stability factor of the bullet.... We normally strive for an SF of about 1.5 - 2.0, while the Military use about 2.5.... A value below 1.0 is unstable (zero means no spin) and above about 4-5 the bullet is considered "overspun".... So, it is not the twist rate PER SE that governs the amount of drift, but how that relates to what is required for that bullet.... ie the SF (sometimes called the SG)…. I know of no calculator that gives the SF for pellets....

Here is the formula I found to calculate the amount of spin drift....

Spin drift = 1.25 x (SG + 1.2) x TOF ^ 1.83

Start by raising your time of flight to the power of 1.83. If the time of flight is 1 second, then (1 ^ 1.83) = 1.... If the SG (SF) of our bullet and gun is 1.5, then the equation becomes: Drift = 1.25 x (1.5+1.2) x 1 for a result of 3.375"....This means in this example, the bullet will drift 3.375" inches to the left or right depending on which twist the gun barrel has....

So, to be able to calculate the amount of Spin Drift, we first need the Time of Flight.... That depends on the MV and BC, and here are a few examples....



For nearly all of our shooting with pellets, the Time of Flight is under 1/2 sec.... and what most of us would consider very long range shooting with bullets would still have a Time of Flight of under 1 sec.... At 1000 yards, it might approach 4 seconds, but let's look at a ToF of under 1 second first.... Once you know the ToF, you need to know the Stablity Factor of the bullet in your barrel, at your velocity.... For bullets (not pellets), you can get that from the Kolbe Twist Calculator which you can find here....

http://www.geoffrey-kolbe.com/barrel_twist.htm

You will need to input the dimensions of the bullet, the twist rate of your barrel, and then read your SF from the graph.... Then use the line that most closely matches that SF (or interpotate, ie guess, something in between) in the chart below....



For example, from the first chart, a bullet with a BC of 0.20, starting at a MV of 900 fps (the yellow line), would take about 0.5 sec. to reach about 150 yards.... If that bullet had an SF = 2.0, with a ToF of 0.5 sec. the Spin Drift would be just over 1".... As you can see, we are not talking a huge effect, but if you are sighted at 50 yards, and shooting at 150, you might miss by 1/2" or so.... Now let's look at what happens at really extreme ranges....



Let say you had a super-slippery bullet with a BC of 0.400, and you launched it at 1000 fps.... The ToF would be 3.7 sec.... If you had the perfect twist rate to give it an SF = 1.5 at that MV, you are still looking at a Spin Drift of over 3 feet.... 

Does that mean you will never hit anything at that distance?.... While it could be hugely important for a sniper that has to make that first shot, in practical terms, spin drift means NOTHING for our shooting.... You simply sight in at the range you are shooting, and the spin drift just becomes part of that process....

So, bottom line is.... for 99.9% of airgunning spin drift doesn't matter.... 

Bob

[tnt76]

Bob, could this be compared to asymmetric thrust or "Prop Walk" in boats?  The top or "shallowest" point in the props rotation has less "pressure" on it than the bottom or "deeper" point, creating a transverse thrust in the direction depending if a clockwise or counter-clockwise prop is used.

[rsterne]

Not really.... When you push on a Gyroscope in one direction, it reacts by the axis moving at 90 deg. to the force applied.... Which direction depends on the direction of rotation.... As I understand it, gravity supplies the "push" (actually a pull downwards), and the reaction of the bullet is to yaw sideways.... This causes a deflection in the trajectory, to the right with a right hand twist and to the left with a left hand twist.... It's not strictly accurate, but if you double the distance, you get about 4 times the spin drift.... In that respect it is similar to wind drift, but the crosswind is NOT the cause, it is a separate phenomenon....

Realistically it is only an issue if you sight in at one range and then shoot at a further distance.... If you can sight in at the range you are shooting, since it is a constant for a given bullet and velocity from your gun, it gets adjusted for in the sighting operation....

Bob

[rkr]

Bob, since you have the math can you calculate me an example that's been puzzling me. I have an Evanix Sniper .45 with a barrel that has 15" twist rate (way too much) causing SF of about 15 IIRC when shooting EPP-UGs. Now I can make the gun group at 50M but when moving to 100M it's hit and miss. Can you check how much the spin drift (50M vs. 100M) is in this scenario versus a scenario where the SF would be more normal in a 1.5-2.5 range if the barrel had a proper twist rate? What I'm trying to figure out is if there's a point where things start to get out of hands with too fast twist rates.