# Time of Flight vs Ballistic Coefficient.

Discussion in 'Rifles, Bullets, Barrels & Ballistics' started by Michael Eichele, Oct 28, 2006.

1. ### Michael EicheleWell-Known Member

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In an effort to free the highjacked thread, I offer this example.

Please note first that the factors that go into wind drift are VERY complex and are not always subject to known mathematical formulas. I say known, because there is a mathematical formula for everything, we just dont always have either the right variables or havent yet figured out how to incorporate certain variables into an equasion. In other words, accurate drift can be always be figured by using math, just not with always with the math we use at this stage in our understanding.

So sometimes, in certain circumstances, a ballistic calculator wont give us a perfect figure, however they can be darn close much of the time. Just for kicks, look at the example below.

Bullet #1: BC of .500 at 3000 FPS at 1K drifts 95.1" with a TOF of 1.5297 sec.

Bullet #2: BC of .400 at 3400 FPS at 1K drifts 110.7" with less of a TOF (1.4933)

Would you say that BC has an effect on wind drift??

2. ### Michael EicheleWell-Known Member

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Also, the calculations in The Reloaders Archive DO NOT use time of flight in any way to calculate wind drift. The calculations are also as accurate as any other program, and in most cases very close if not spot on in real life shooting.

3. ### James JonesWell-Known Member

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makes sense to me , the whole math and getting into the theory makes my brain hurt so I just look and watch what the guys winning the comps do , they must be doing somthing right?
Good info , I think that mnore guys should chime in and see what kind of Ideas other folks have on this topic. Its the kinda topic that guys that are new to the Long Range game could learn from or at least clear up alot of misconceptions.

4. ### BuffalobobWriters Guild

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I agree with your first post as to the extremely complicated physics of windage compared to drop and that almost all ballistics are empirical.

As to your second post you probably want to revise it a little. Kinematics is fairly straghtforward and there are ways one can avoid actually writing "t" such as using "x/v", but a person who knows a passing amount of physics can quickly substitute terms and "find" the terms.

Secondly, my two cents, assuming a 10 mph crosswind and a 3000 fps muzzle velocity, what the bullet actually experiences is a vector wind force not two scalars. That vector is {3000fps i + 14.7 fps j}. Consequently, shape is important for wind drift.

5. ### Michael EicheleWell-Known Member

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I am not sure why I should revise my second post. The calculations used in my program dont use TOF. This is a fact.

[ QUOTE ]
Consequently, shape is important for wind drift.

[/ QUOTE ]

I agree.

6. ### Brown DogWriters Guild

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meichele,

I'm not clear why there seems to be an assumption that a bullet's nose-on BC is the only figure to be used when assessing its lateral wind resistance (and therefore the force it will experience from a lateral wind).

If it were possible to make 2 (unspun) bullets of identical nose-on BC but with different cross sectional shapes (for example one a conventional tube and the other with a square cross section such that it presented a vertical flat surface to the wind) why is it assumed that both bullets will be pushed the same amount by a lateral wind? ......despite identical nose-on BC's, I think we would agree that the flat sided bullet would have a greater lateral drag coefficient and consequently be pushed further.

My point is that same calibre bullets are all essentially similar bullet-diameter tubes when side on; and I suspect that their lateral drag coefficients will be very similar (with values certainly far closer than their nose-on values).

So, given that pocket small arms ballistic calculators are basing their calcs on simple algorithms (ie, I don’t think any of them are doing 6 DOF trajectory modelling /ubbthreads/images/graemlins/smile.gif) I can’t see how the nose-on BC can be taken to have primary relevance

As I said on the other thread...the fact that the small arms ballistic programs that we’re using are indicating drastically different winddrift due to higher nose-on BC is not proof; they give the answers they were written to give!

I don’t doubt that the high nose-on BC bullets will outperform the lower ones…..and, I hope, from the reasoning above you will see that I don’t subscribe to the simple TOF differential theory……….but I cannot see why a nose on BC is being solely used in calculations that actually should involve the bullets lateral drag coefficient ...an algorithm 'fudging' an assumed lateral BC based on, say, the BC of a sideways presented 'standard bullet' (they're all essentially similar bullet-diameter tubes when side on) and the actual bullet's nose on BC as well as the actual wind angle would be more accurate.

……I suspect that (when considering the effects of lateral winds) such programs are treating bullets as spherical point masses. …..and as a result their data outputs are skewed in favour of the high nose-on BC bullets.

...and everyone believes what their computer says /ubbthreads/images/graemlins/smile.gif a bit like following a GPS into a lake /ubbthreads/images/graemlins/grin.gif

Will any of this affect the price of fish? No, but I admit that I find it interesting to be forced to think about these things!

I’m away for the next 4 days, but will be keen to read your thoughts on my return ....particularly if you are able to tell me that the current programs do factor lateral drag against wind angle!

All the best

Matt

7. ### bsbWell-Known Member

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wowzer! what about the bullet going through fog or light rain? /ubbthreads/images/graemlins/wink.gif

8. ### CatShooterWell-Known Member

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Meichele...

I wonder what software you are using.

I have found many errors in Sierra's Infinity program in regards to windage - errors where lower BC bullets at the same speed had less wind drift (WHAT???).

I have contacted them on this and they mumble something about "... in the next upgrade".

The Sierra software is a 20 year old antique, and it is constantly being repaired, glued, and patched with software bandaids.

I have mostly relied of RSI software. It has yet to let me down, or give me solutions that are rediculous!

9. ### nsbMember

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[ QUOTE ]
If it were possible to make 2 (unspun) bullets of identical nose-on BC but with different cross sectional shapes (for example one a conventional tube and the other with a square cross section such that it presented a vertical flat surface to the wind)

[/ QUOTE ]

And if Mike Tyson had a titanium skull, he'd still be the champ. /ubbthreads/images/graemlins/cool.gif

I don't think what you're proposing is possible. That's like saying "If a car going 60mph passed a car going 80mph, then wouldn't 60mph be faster than 80mph?" Well, yeah, but it can't happen. At such point that you changed the shape from round to square, you have changed (lowered) the BC. Now, I'm not going to say that you couldn't be right on some quantum physics level, but you'll need to take that up with Stephen Hawking, because there might be parallel 2 dimensional universes where ballistic and aerodynamics apply differently.

But on a more practical level: Is there a gun that can throw a square bullet that wouldn't tumble? It seems to me that by basic design, all bullets are round in shape.

I've tried, but I can't even go into the imaginary world where a square bullet could be shot, because of the turbulence it would throw. It would probably hit the ground after 100 yards. Or maybe even corkscrew down the range since the corners would be like fins. So yes, an object with flat sides would have different lateral forces at work, but it would also have a lower BC than an object without flat sides.

10. ### wombat6New Member

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I'm no expert in ballistics or anything, but I believe what is happening is the wind "steers" the bullet more than it pushes it. I'm sure the TOF and lateral cross section do have a bearing on how much a bullet will drift, but they are not the primary cause of it. My guess is the wave of compressed air ahead of the bullet acts against the wind, steering the bullet off course. More aerodynamically efficient bullets should tend to cut through the wind by virtue of less frontal drag. Less efficient bullets with huge shock waves off of the nose provide more for the wind to act against.

I use Load From a Disk and Silhouette Ballistics to do my initial predictions, and both programs seem to give very accurate wind data. Both programs use ballistic coefficient as the primary variable. I guess I don't care too much about what the program says as long as I can verify it on the range. So far it's worked reliably for me out to 1,000 yards.

Just to add to the debate, when I input a projectile velocity between 900-1000 fps or so, the wind drift is very minimal at all distances. The same projectile will drift significantly more when propelled to even 1,100-1,300 fps. In fact it won't drift as well again until velocity reaches 2,200-2,300 fps or higher. I'm not sure exactly how complex the wind drift formula is, nor how accurate this prediction. I have no subsonic guns right now, so I haven't been able to verify this phenomenon myself. Any .300 whisper shooters here?

11. ### Michael EicheleWell-Known Member

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BD,

I do not dissagree with you. The fact is, at this stage in our understanding of this topic, we dont have all the answers. There are answers there, we just dont understand them yet and havent figured them out. Hence my original post.

[ QUOTE ]
Please note first that the factors that go into wind drift are VERY complex and are not always subject to known mathematical formulas. I say known, because there is a mathematical formula for everything, we just dont always have either the right variables or havent yet figured out how to incorporate certain variables into an equasion. In other words, accurate drift can be always be figured by using math, just not with always with the math we use at this stage in our understanding.

[/ QUOTE ]

Many calculators will get you close in most circumstances, but there are more variables in wind drift in the real world than we have equasions for so modern calculators are bound to only be close some of the time, right on in others, and way off in other circumstances.

Please note: I am not an authourity on this subject. This is all theory and speculation here. It is however a fun topic to disscuss and very informative as to what others know and think.

12. ### JBMWell-Known Member

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[ QUOTE ]

I'm not clear why there seems to be an assumption that a bullet's nose-on BC is the only figure to be used when assessing its lateral wind resistance (and therefore the force it will experience from a lateral wind).

[/ QUOTE ]

For most bullets you can buy, the BC is all you have. What the bullet "sees" (or feels) is the total velocity relative to the air. If you it is going downrange at 3000 f/s and there is a cross wind of 10 mph (call it 15 f/s for the fun of it), the bullet sees a total velocity relative to the wind at a very small angle off the nose (arctan of 15/3000). The wind isn't hitting the side of the bullet.

[ QUOTE ]

If it were possible to make 2 (unspun) bullets of identical nose-on BC but with different cross sectional shapes (for example one a conventional tube and the other with a square cross section such that it presented a vertical flat surface to the wind) why is it assumed that both bullets will be pushed the same amount by a lateral wind? ......despite identical nose-on BC's, I think we would agree that the flat sided bullet would have a greater lateral drag coefficient and consequently be pushed further.

My point is that same calibre bullets are all essentially similar bullet-diameter tubes when side on; and I suspect that their lateral drag coefficients will be very similar (with values certainly far closer than their nose-on values).

So, given that pocket small arms ballistic calculators are basing their calcs on simple algorithms (ie, I don’t think any of them are doing 6 DOF trajectory modelling /ubbthreads/images/graemlins/smile.gif) I can’t see how the nose-on BC can be taken to have primary relevance

[/ QUOTE ]

The modified point mass does, by using the change in CD (doesn't use BC) for small angles relative to the wind which is what you see for small wind speeds.

This value is of the form: CD0 + alpha^2*CDA2

So as the angle of attack, angle of bullet centerline relative to velocity vector relative to air, increases so does the CD.

[ QUOTE ]

As I said on the other thread...the fact that the small arms ballistic programs that we’re using are indicating drastically different winddrift due to higher nose-on BC is not proof; they give the answers they were written to give!

[/ QUOTE ]

Or they are just wrong...

[ QUOTE ]

I don’t doubt that the high nose-on BC bullets will outperform the lower ones…..and, I hope, from the reasoning above you will see that I don’t subscribe to the simple TOF differential theory……….but I cannot see why a nose on BC is being solely used in calculations that actually should involve the bullets lateral drag coefficient ...an algorithm 'fudging' an assumed lateral BC based on, say, the BC of a sideways presented 'standard bullet' (they're all essentially similar bullet-diameter tubes when side on) and the actual bullet's nose on BC as well as the actual wind angle would be more accurate.

……I suspect that (when considering the effects of lateral winds) such programs are treating bullets as spherical point masses. …..and as a result their data outputs are skewed in favour of the high nose-on BC bullets.

[/ QUOTE ]

I don't know of any that do this. There may be, but the ones that I've seen do the typical aerodynamics formula. The force on the bullet is proportional to the CD and the difference between the velocity and wind vectors. I have the derivation here.

13. ### Brown DogWriters Guild

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All,

Some interesting perspectives!

Michael,

Thanks for your thoughts...I enjoy stretching the unused grey matter on this!

JBM,

Absolutely clear; very many thanks! ....(and I promise to be less cynical about 'PDA' windrift data outputs from now on! /ubbthreads/images/graemlins/smile.gif /ubbthreads/images/graemlins/smile.gif)

..just flew back down from Scotland...despite all this theory and thought, I still managed to biff 2 wind calls (still landing both bullets forward of the diaphragm...but not as far forward as I would have chosen /ubbthreads/images/graemlins/smirk.gif /ubbthreads/images/graemlins/smile.gif) me (on the right) and a pal at the conclusion of our final (and most testing/exciting) stalk yesterday:

14. ### edgeWell-Known Member

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How cool is that, to be able to hunt with Sherlock Holmes!