Range Report Windage Effects (Ballistic Calculations)

[bronco9588]

I am trying to explore the effects of wind on the ballistic path.

There are two effects I am trying to hone in on:

1) Shape pressure drag, or the push on the bullet that causes left and right drift.

2) Magnus effect that causes an up down lift on the projectile due to spin.

Right now I am not so worried about 2, but anybody have any good formulas that are accepted for bullet drift?

 

[Lowlight]

Re: Windage Effects

See Applied Ballistics from Bryan Litz,

Formula wise, most use a Ballistic calculator which does the math for you.

More and more you'll start to see the discussions around dissimilar wind effects growing. Right now the talk is low and on the fringe but I suspect it will begin to become more mainstream in the coming year.

 

[bronco9588]

Re: Windage Effects

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: Lowlight</div><div class="ubbcode-body">See Applied Ballistics from Bryan Litz,

Formula wise, most use a Ballistic calculator which does the math for you.

More and more you'll start to see the discussions around dissimilar wind effects growing. Right now the talk is low and on the fringe but I suspect it will begin to become more mainstream in the coming year. </div></div>

1) I am looking for the formula behind the ballistic calculator as a function of BC, weight of bullet, and wind strength.

2) Do you recommend any other books for the study such as Art Pejsa book?

3) When you say dissimilar wind, are you inferring potential differences in the wind vectors strength and magnitude along the ballistic path?

a) If so... I think there maybe a way to account for dissimilar wind along the ballistic path by using an iterative solution like all ballistic calculators coupled with wind speed at 4 or 5 locations along the ballistic path.

 

[Lowlight]

Re: Windage Effects

i have Pesja's book, doesn't hurt to have more than one opinion.

Most are using Bryan's now, parts 1 & 2. He is currently behind a lot of the calculations. He is also a member here, you can pm him.

No, dissimilar wind in the effects of wind drift differing from right or left based on the twist of the rifle. One set of adjustments for left, another set for right. Basically including your magnus effect, changing how the bullet drifts.

Wind is never constant along the flight of bullet that is a given. Getting actual readings along the path in real time, that is another story. Ebbs and Flows, doesn't really allow for it.

 

[BryanLitz]

Re: Windage Effects

I think Frank's talking about spin drift

My book is good for the application, and even has a part about calculating effects of multiple winds based on time of flight in segments.

However, it was never intended to contain the full ballistic equations of motion required to write a ballistic solver from scratch. If you want that level, I recommend Modern Exterior Ballistics by Robert McCoy. Be sure to download the extensive errata sheet, despite which, this is the authority on the subject at the fundamental level. Again my book starts where McCoy leaves off and focuses on application.

Good luck,
-Bryan

 

[bronco9588]

Re: Windage Effects

Bryan,

Thanks for the info. I will probably just go ahead and buy all three and evaluate the claims over the next month.

Long story short... I am trying to isolate crosswind shape drag, from magnus effect, from spin drift. The funny thing is Coriolis was the easy part of the calculation.

 

[bronco9588]

Re: Windage Effects

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: bronco9588</div><div class="ubbcode-body">Bryan,

Thanks for the info. I will probably just go ahead and buy all three and evaluate the claims over the next month.

Long story short... I am trying to isolate crosswind shape drag, from magnus effect, from spin drift. The funny thing is Coriolis was the easy part of the calculation. </div></div>

Tried to purchase, but it is declining my card. "Reason for decline: The merchant login ID or password is invalid or the account is inactive."

 

[bronco9588]

Re: Windage Effects

So I have done some reading in Modern Exterior Ballistics by McCoy to get a better understanding of windage. On pages 158 and 159 in section 7.4 it says the following:

"The deflection due to a constant crosswind, Wz, is Z=Wz*(t-X/Vxo)."

This is basically saying the time the bullet was slowed down is the amount the bullet rides with the wind.

"[The] equation also shows that if a sustainer rocket, whose thrust precisely equals the drag force were added to the base of the projectile the lag time would vanish and there would be no deflection due to crosswind. This concept is referred to as "automet," and has been used for ordnance projectile designs that required absolute minimum sensitivity to crosswind. If the rocket thrust exceeds the drag force, the lag time will be negative, and we note that equation correctly predicts upwind deflection observed for high thrust rockets in crosswinds."

I am not saying that the book is wrong, but I am having a hard time visualizing the horizontal fluid flow here. If there is a crosswind, I feel that we should be able to superimpose frontal velocity drag from crosswind drag, where the crosswind drag "pushes" the bullet with the wind due to a pressure differential between the windward side and the leeward side of the projectile. (The front and side would have differing coefficients of drag). According to my (possibly incorrect) theory, The windage drift vector would always be inline with the wind and therefore a bullet with no deceleration forward will still be effected via windage because that force is independent of the frontal force.

Moreover, the author claims that a rocket projectile goes upwind. I accept this fact because a rocket with a center of gravity in front of a center of pressure (which makes the rocket stable if there is no control system) acts like an inverted pendulum and will point into the apparent wind. However, I see this as a completely different set of physics.

If anybody can explain this phenomena to me, bonus points, because I am a mechanical engineering grad student, and I am still scratching my head after banging it against a wall for several days.

 

[Bearwalk]

Re: Windage Effects

Bronco, where you are going wrong is assuming that the windage effects are independent of the foward motion. In fact, x, y and z travel are dependent of each other. Please refer to McCoy's chapter on 3DOF point mass where he presents the eauations of motion both with to repsect to time and x. They are <span style="font-style: italic">coupled</span> non-linear ODE's which can not be solved analytically. Anyway, I digress, my point is that travel in all three planes are not independent of any other.

Now, if I can take the liberty to digress further, I have a couple of suggestions that may help you on getting to where you want to be, but there is pain involved. I suggest building a point mass solver using Runge Kutta 4 NI. I'll be happy to help as I just finished mine....I did it in excel with only a couple of VBA calls. Setting up this solution will bring you to a level of understanding that only a few can appreciate! Along the way you are going to become intimately familiar with those equations of motion which governs all things ballistically speaking. After solving for your trajectory add in the equations for spin drift and coriolis to see their effects and answer a lot of your questions.

In addition to MCoy's book, please see "Ballistics" by Carlucci. Also a good tratment of the subject, though not as easy to read as McCoy's. He goes in to more detail on the derivations than MCoy did and covers some other topics as well.

Pejas's book presents an analytical solution, which I also did in excel, but be warned that his book is hard to follow if you are trying to set up an actual solution and is written by a mathmatician, not an engineer/ballistician. He takes plenty of liberty with unneccessary shortcuts...enough to drive one mad. Ironically, it took me longer to set up a solution using his methodology than doing a point mass solver, though I do admit that the accuracy was good if you take the time to set up an adequate drag function...only through the transonic zone, though, and for low (see zero) angle fire. It falls apart quickly if you push it beyond these limts.

Sorry for the long reply...and let me know if you decide to go any further with this.

 

[bronco9588]

Re: Windage Effects

Bearwalk,

Thanks for the info as it gets me on my way. I have done a point mass calculation via small incremental time steps (for loop in Matlab) and physics projectile motion equations assuming windage, gravity, inclination, amongst other things. I have not tried RK4 or RK45 partly because I didn't really understand it that well in Numerical Analysis class. With a time step of .00001 and a maximum Dx of 8 cm per iteration, it takes my calculator about 3 seconds to solve. I don't know if RK is faster, but I think that its something I am willing to do.

I think McCoy actually dives into how to do a RK analysis which will be helpful. My calculator also has the tables and accounts for humidity, temperature, and pressure. It still needs spin drift and Coriolis which I hope McCoy goes into, but I haven't read that far.

Pejsa's book is terrible and I question why the publisher did not have someone go and block quote the equations and edit some of the layout of the book. I thought Pesja was a rocket scientist, not a mathematician, but I am probably wrong. I would not feel bad if it feel out the window of my car.

I will look into Carlucci.

I do appreciate the long reply and am curious how you got into the same project. I also would be interested in empirically validating my program and would be interested in long distance (1000 yrd+) beta testers.

 

[Bearwalk]

Re: Windage Effects

Bronco,

So, you are well on your way. My bad, I should have known from your questions that you were up to something.

I would recommend you do your solution on x, not t. It will be easier to set up your trajectory tables and to do angled fire solutions.

While we're on angled fire, I recommend not rotating your axis', BTW...keep y perpinduclar to the earth. I found this way much easier. I then just bookkeep the difference in height from the target at any given range. To get come-ups the path needs to be multiplied by the cosine up the site angle, though. Most programs out there do not do this, BTW. So, while they're path or trajectory may be correct, the shooter is left with an additional step to get the correct come-ups.

RK4 is fairly straigth-forward and JBM has the equations for non-liner coupled ODE's posted on his website. I did do some head scratching on x not actually appearing in any of the equ's of motion, but just set up your functions as they are in MCoys book, and set-up up your K constants on Vx, Vy, and Vz and you will be GTG. I will try to write up my RK4 equations and post here, but I am really buried at work so it might not happen immediately.

Also, no need for such a small time step (or the equivalent x). At least with RK4, I found the equivalent of .001s to be plenty good even in the transonic and subsonic zones.

Ahh, as for how I got in to this... I have a bachelors and masters in aerospace eng from VT. I spent a good portion of my career modeling flow over airfoils and jet engine thermodynamics for one of the large (see largest ) .gov contractors. Eventually said employer talked me in to getting an MBA. I now build financial and economic models which, believe it or not, are incredibly complex.

So, I model ballistics to suppoprt my shooting, and because they're are certain "features" I need that are not available in any of the commercial packages. I still use several extensively, though, especially LB3 (3 months or so), Shooter, Ballistics FTE, and JBM.

 

[bronco9588]

Re: Windage Effects

Sweet, it sounds like you will be able to help me out when I get stuck on some of the harder concepts.

1) Definitely going to do the calculator as a function of X, but I am stuck in this world where I only like t. Again, I mathematically need to go back and challenge myself.

2) I am leaving my x z plane tangential to the surface of the earth with y axis being normal. I have done a translation that plots x-axis as the optical plane just to get a visualization of the amount of click I would need. I have not run extreme angles, but from what you are saying is basically dy at target times cos of the incline? That makes good sense. I haven't seen a need to do that only because I have run mild inclines. Will try out something like 60 degrees and see what I get.

3) With all my codes I would love to do an error analysis, but I feel that it would take several days and not really show much returns. Good to know that such a time step is not really needed.

4) My story is that I have always been a gun enthusiast, but I bought a 308 rifle right around Obama's election and rounds were 1.50 a shot. I did the numbers and got into reloading. Since then I have got into a study on ballistics and precision. Luckily, I am at the Naval Postgraduate School and have some time on my hands between classes. I think what really got me interested in the external ballistics study was my fluids class. Did you spend most of your time at Boeing? researching compressor and turbine vanes?

 

[Bearwalk]

Re: Windage Effects

1) Mathematically, it is more intuitive to set-up up NI on a time step, I agree. This will certainly solve your equations just as well. When you complete your trajectory solutions table, though, just know that you will often have to interpolate between ranges for the exact one you are looking for. Not the end of the world, but an extra step for sure.

2) I didn't say this as well as I should have. For angled fire, you will need to keep track of your bullet absolute vertical position, y, and at the corresponding x, the height of the target, HT. The difference, y-HT, will give you "uncorrected come-ups". Multiply this value by the cosine of the angle of site to get actual corrections for your scope. I do a lot of shooting in the Adirondacks, so angled fire is important to me, BTW. You can verify the above at home by building in to your model the ability to enter barrel super-elevation and then re-plotting the trajectory with both corrected and uncorrected come-ups. You'll see what I mean.

4) Congrats on NPS! That's a big deal. If you haven't already, get a class the covers turbulent compressible flow. You won't regret it. The solutions to turbulent flow apply to many other areas of the world, including chaos theory of financial markets. LOL! Somewhat pertinent to today's world.

I spent time in both turbine and compressor design, but this was a maturing field at the time with limited new ground to cover. I moved over to overall thermo performance of the engine where the models needed constant revising and re-building to keep up with the pace of new military engines and their derivatives. I finally had new horizons. By now have figured out by now that I go back to the cold war days, bro, but don't let that fool you, I can still get around.

I may try to get to the RK4 equations today. I think they will help you a lot.

 

[bronco9588]

Re: Windage Effects

Bear,

Wow... I was really comfortable in chapter 8 with point mass trajectory and then I felt like Ochochinco being hit by Ray Lewis in chapter 9. It was like boom. I have long given up on deriving things people tell me, but I had no idea there was so much to ballistics. Point mass makes sense, but I don't think that it is reasonable for me to make a pure 6 Degrees of Freedom Model because all the different coefficients of drags. I count 11 different coefficients. Is it reasonable to be able to call up Sierra, or Nosler, or Berger and get these values? It would be nice, but I feel that everybody is stuck on Ballistic Coefficients, let alone Cd values at different velocities. I wonder if there is a place I could send a projectile to have evaluated?

Anyways p. 216 of McCoy says: "the 6-DOF predicted yaw of repose and the right hand drift, respectively, for the .308... Modified point-mass trajectories were also run for the same three rifling twist rates, and the results were compared against the six degrees-of-freedom solutions. <span style="font-weight: bold">The modified point-mass values and the 6-DOF values agreed so closely that the plots showed no significant difference</span>" This is pretty good. I am guessing the only difference between the point mass and the modified point mass is spin drift? I am assuming he is referring to equations 9.59 and 9.60? If so, there are a couple coefficients that are mistyped or not included in the appendix referred to for that round. Specifically, what is C_N_p*alpha (Cnpa) and C_l_delta (Cld)?

It sounds like I am pretty close to a very accurate calculator with the modified point mass analysis. Anything more severe would be really expensive for which to get data. After this, it will be fun to go validate. I imagine that windage, drag, Coriolis, gravity, and spin drift covers all the forces that would noticeably effect the ballistic path in relation to the error introduced by the shooter, ammunition, and internal ballistics.

 

[Bearwalk]

Re: Windage Effects

Ahh... I should have warned you to stop at Chapter 8. LOL! Also, regarding those equations, there is a great errata document online for Bob's book. He passed on before he could fully edit his book, but several of his colleagues did it for him. Google it and if you can't find it, I'll email you a copy.. it's a must have.

You're right, even if you had the resources to gather up all the other coefficents for your particular bullets, the gains in trajectory prediction for 6DOF are fairly marginal as McCoy points out. Now, if you were designing control systems for ICBM's to travel 1500 miles, you might need that additional precision, but then you would also have the resources to do so...

But hey, if you can tackle it don't let me slow you down!

I haven't gone into modified point mass since I have had very good luck with Bryan's Coriolis and spin drift corrections on my point mass model. They are very easily applied to your calculated trajectory as a correction. IIRC, McCoy also derive similiar equations in his book.

I forgot to ask how you are handling your drag functions. I start with standard functions, G5 or G7, and scale them to match my field testing. So far, I have pretty good functions for several SMK's and SGK's. Bryan's data is also an excellent resource here. I have recently found several SMK's to match his published drag functions very very closely. For SGK's I like to start with G5, but we're really splitting hairs here since major differences between G5 and G7 don't show up until you've gone very transonic and I'm only pushing my rifles/projectiles out to M1.3 or so..

 

[bronco9588]

Re: Windage Effects

I feel like the only part that I am missing would be the spin drift part, and I don't feel very satisfied with McCoy's book on this. You mention Bryan? I am assuming Bryan Litz book covers a good solution.

Right now I am just working on the calculator. I didn't bring any of my guns out here to test the calculator

. I figured CA gun laws would have been hell to deal with. Anyways, your question about dealing with drag is a good one. I would have to take a look at the code which is at school. Currently, I am only working with G1 curves and scaling them the entire curve with the bullet manufacturers BC over the G1 BC, but I think I may have done this incorrectly in the code and will probably take a look at it on Tuesday. I am using the G1 curve because it is the BC most commonly reported, but my calculator can use all the different types of curves. Honestly, I hate the concept of BC and it really only makes sense before the days of personal computers. I would love to get the drag as a function of velocity with reported speed of sound for the atmosphere the projectile was measured in (Length/ Time not Ma#). I feel that as a consumer of a projectile I should have access to this information. They must have some way of measuring BC?

Anyways, I think I maybe able to populate my own Cd as a function of velocity curves. I would like to get 2 or 3 chronographs and make several tens of shots through the setup with the same projectile. Maybe tailor high velocity shots all the way down to low velocity shots. Theoretically, if the chronographs are accurate enough and I know the spacing between the two of them, I should be able to populate my own curve. What that spacing is and the accuracy of the best chronograph, IDK?, but I figure this method would be far more superior that local BC scaling along the curve.

My email is [email protected] for the errata document.

 

[mouse07410]

Re: Windage Effects

@bronco9588, One interpretation of BC is how much better or worse a given projectile flies through the air compared to the standard (reference) projectile (i.e., G1 or G7). As such BC is also useful (as Bryan Litz pointed out) in comparing different projectiles (without it, how would you compare - print out drag functions for both and compare its coefficients?). Populating your own Cd as a function of Mach curve sounds fine (I'd use Mach rather than velocity).

Lastly, IMHO limiting a calculator (presumably intended for LR and ELR) to G1 is suboptimal.

@Bearwalk, I wonder how your calculator performs in transonic region. Otherwise your approach is what I'd do myself. I've been toying with the idea of writing my calculator (basing it on the freeware GEBC-1.07 under GPL license, which I've fixed for Snow Leopard - mainly for the already-provided GUI). It seems to lack some corrections that I consider important. I'd like to talk to you, and maybe get some help. This is a future project, now my hands are full with other things to take care of, and Bullet Flight (together with Ballistic FTE, and JBM Online

) satisfy my humble needs.

 

[bronco9588]

Re: Windage Effects

Mouse,

I definitely agree with you on the BC stuff and would like to use G7 curve. My problem is that 1) I don't have access to empirical data cause my Guns are in MD with the folks and I was terrified of CA's gun policy (partly due to not being educated on the matter). 2) I used Nosler bullets and they only report G1.

I know what BCs mean, but I would much rather buy a projectile based on Cd curves rather than a single BC that will not scale a baseline curve accurately, but in the development of my code, I expect this input to be incorrect. Right now I think I have it scaled by sectional density, because it was available? I cant remember but I know its not right. I understand differential scaling, as some manufacturers report BC along the Cd curve. However, IMHO, I do not like this because drag is or should be based on Cd, not how well a bullets Cd compares to a baseline projectile. If you shoot the bullet, you measure Cd anyways. Besides projectile comparison, why convert from Cd to BC to be converted back to Cd just to do an analysis. Seems kinda backwards. Moreover, different companies report different sections of the curve and my hunch is that each company is trying to get the edge on another by reporting sections of the curve that get the best BC. Not really knocking those who use it, but rather questioning why we have not gotten off the system. I think it would be amazing if instead of load data, that there be Cd data in a database for projectiles.

I am still wondering who can analyze a projectile for me because I feel that a chronograph may not have a high enough resolution. It would be pretty sick to have some sort of Doppler system to do the readings for me.

 

[Bearwalk]

Re: Windage Effects

Mouse,

I hear what your are saying about BC, but I also hate the concept. Mostly because it's a dated effort to reduce calculation labor before the days of PC's, etc. It's one redeeming feature, the ability for comaparison of projectiles has been badly abused and hijacked by marketing types. I really hate discussing BC and would rather talk about drag levels through a particualr Mach zone. I also dream of the day bullet manufs. publish complete drag functions! Cut out the middle man so-to-speak. But, I also realize this is not going to happen in my lifetime. LOL!

My solver does very well all the way deep into the subsonic realms. As I was de-bugging, I kept comparing to JBM, and kept getting closer and closer until I finally matched JBM exactly. I don't mean +- 1% or .5%, but .1% or less. Angled fire, cold days, hot days, 100 yards, 1500 yards, doesn't matter. So, I can say with certainty that JBM does his point mass solver properly! In all seriousness, feeling very good about the solver's capabilities all the trhough the trans and subsonic regions.

But, that just means my solver is working ok....1/2 way there so-to-speak. Right now working diligently on drag functions, so that I am not feeding garbage into it.

Bronco, I did mean Bryan Litz's book. I would highly recommend using Bryan's data for any projectile's that match your interest's. He has done a lot of the heavy lifting here. I admit to having done some tweaking, but mostly for bullets that I gave a spin rate to that was much higher than normal, and/or in the trans-subsonic regions where admittedly, Bryan has not extended his testing to.

Oh, and it goes for both of you that I am willing to help out in anyway I can. Please do not hesitate...I absolutely love this shit. It helps get me back to engineering, which I miss, and when I can't go out and shoot, modeling is a viable substitute.

Now, maybe we could do a group buy on some doppler time....

 

[mouse07410]

Re: Windage Effects

@bronco, a quick comment: Bryan Litz provides stepped G7 BC (and Cd

) for a whole truckload of bullets - including Nosler. Take a look at his Applied Ballistics book 2nd edition (and check Group Buy for it

). So no need to rely on the measly data form the manufacturer.

My only issue with those is that Bryan didn't measure down to transonic. On the other hand, his range was 600m, so there was no way (I guess) he could extend the measurements beyond about M 1.3...

 

[bronco9588]

Re: Windage Effects

What if Bryan were to change his load and lower the power to start the bullet at really slow speeds?

 

[bronco9588]

Re: Windage Effects

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: Bearwalk</div><div class="ubbcode-body">and when I can't go out and shoot, modeling is a viable substitute.

Now, maybe we could do a group buy on some doppler time.... </div></div>

1) This gets me through my separation
2) Very yes on the doppler.

 

[bronco9588]

Re: Windage Effects

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: Bearwalk</div><div class="ubbcode-body">
In addition to MCoy's book, please see "Ballistics" by Carlucci. Also a good tratment of the subject, though not as easy to read as McCoy's. He goes in to more detail on the derivations than MCoy did and covers some other topics as well.
</div></div>

Just looked up Carlucci and I need to refinance the car! I just picked up Bryan's book and hopefully it will yield some good information.

 

[mouse07410]

Re: Windage Effects

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: bronco9588</div><div class="ubbcode-body">What if Bryan were to change his load and lower the power to start the bullet at really slow speeds?</div></div>
I don't really know. But I recall my discussion with him on a related subject, where he pointed out that behavior of a projectile that slowed down from supersonic to subsonic differs from that of a projectile that was launched at a lower (e.g., subsonic) velocity. In any case, Bryan did not try launching his bullets slow...

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: Bearwalk</div><div class="ubbcode-body">Now, maybe we could do a group buy on some doppler time...</div></div>
Hmm... Sounds really great - but somehow I'm not holding my breath...

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: bronco9588</div><div class="ubbcode-body"><div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: Bearwalk</div><div class="ubbcode-body">In addition to MCoy's book, please see "Ballistics" by Carlucci.</div></div>
Just looked up Carlucci and I need to refinance the car!</div></div>
I opened Carlucci, and I need a (metric) ton of Tylenol for my headache! And something for the toothache, that Carlucci is good at causing. McCoy is a nice smooth reading. Carlucci is a ride on a rocky road in a car with square wheels.

 

[tobias]

Re: Windage Effects

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: Bearwalk</div><div class="ubbcode-body">
I also dream of the day bullet manufs. publish complete drag functions! Cut out the middle man so-to-speak. But, I also realize this is not going to happen in my lifetime. LOL!
</div></div>
Lapua provides drag functions for most of their bullets on their homepage. Here's the table for the 167 gr. Scenar, for example:
C_d Mach
0.180 0.000
0.178 0.400
0.154 0.500
0.129 0.600
0.131 0.700
0.136 0.800
0.140 0.825
0.144 0.850
0.153 0.875
0.177 0.900
0.226 0.925
0.260 0.950
0.349 0.975
0.427 1.000
0.450 1.025
0.452 1.050
0.450 1.075
0.447 1.100
0.437 1.150
0.429 1.200
0.418 1.300
0.406 1.400
0.394 1.500
0.382 1.600
0.359 1.800
0.339 2.000
0.321 2.200
0.301 2.400
0.280 2.600
0.250 3.000
0.200 4.000
0.180 5.000

 

[bronco9588]

Re: Windage Effects

Thats pretty sweet... now how about lift force coefficient, spin dampening coefficient, magnus moment coefficient, and pitching moment coefficient?

 

[Bearwalk]

Re: Windage Effects

@Bronco and Mouse - I tried to warn you about Carlucci. Ha! You guys are right, exepensive and hard to read book. Marginal additional info after McCoy. But, still, if you are rounding out the ballstics "library", there are less informative books out there.


@TOB - Thanks for the reminder on Lapua's efforts for which they are to be commended. I have thrown them plenty of "brass" business over the years, but not so much "bullet" business. I should (and will) change that.

 

[bronco9588]

Re: Windage Effects

I bought Bryan's book instead, but he is competing around the world currently so I had to give up on my autographed copy. Hopefully he will have some stuff to add to the thread when he gets back.

 

[bronco9588]

Re: Windage Effects

So I have hit somewhat a brick wall in my quest to tackle higher degree of freedom models. I am trying to tackle spin drift. I think I understand the physics behind spin drift, but am getting lost in the calculations as McCoy does not present any magnus force coefficients for any of his projectiles. Any help or suggestions here would be greatly appreciated? I don't think McCoy is neglecting this input, as it is also important coefficient for modified point mass as well. The force (or coefficient) appears to be the only contributor to left and right movement in the absence of wind (assuming a non-wobbling axis of the bullet).

 

[tobias]

Re: Windage Effects

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: bronco9588</div><div class="ubbcode-body">I think I understand the physics behind spin drift
</div></div>
No offense, but I think you don't.

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: bronco9588</div><div class="ubbcode-body">
but am getting lost in the calculations as McCoy does not present any magnus force coefficients for any of his projectiles. Any help or suggestions here would be greatly appreciated?
</div></div>
The reason for spin drift is the yaw of repose. In chap. 11 McCoy presents formulas for calculating the drift (equ. 11.42 and 11.57), that were derived with only the aerodynamic drag retained. All other forces and moments were neglected.

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: bronco9588</div><div class="ubbcode-body">
I don't think McCoy is neglecting this input,
</div></div>
Yes, he does (in chap. 11).

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: bronco9588</div><div class="ubbcode-body">
The force (or coefficient) appears to be the only contributor to left and right movement in the absence of wind</div></div>
No, that's wrong. As I wrote, it's the yaw of repose, the Magnus effect is much smaller and it acts in the opposite direction!

 

[bronco9588]

Re: Windage Effects

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: tob</div><div class="ubbcode-body">
<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: bronco9588</div><div class="ubbcode-body">
I don't think McCoy is neglecting this input,
</div></div>
Yes, he does (in chap. 11).

</div></div>

soo.. Cn_pa of 9.8 and 9.59 is not calculated in example 9.1?

Thanks for correcting my misconception. Yaw of repose would be the the cross product force you experience when you try to change the orientation of a gyroscope per say? Or is it something else?

 

[tobias]

Re: Windage Effects

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: bronco9588</div><div class="ubbcode-body">
soo.. Cn_pa of 9.8 and 9.59 is not calculated in example 9.1?
</div></div>
Now I get it... That's a good question. I don't know.
I wrote Cn_pa and all other effects (with the exception of aerodynamic drag) are neglected for chap. 11, where analytical formulaes are presented.
I assume, that a 6 dof calculation considers every force and moment, that appears in equ. 9.10 to 9.15, however I also don't find Cn_pa (nor other coefficients, e.g. Cn_q) in appendix A. Maybe McCoy didn't list them or some forces and moments are neglected even for the 6 dof calculations.

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: bronco9588</div><div class="ubbcode-body">
Yaw of repose would be the the cross product force you experience when you try to change the orientation of a gyroscope per say? </div></div>

Yes.
The bullet points to the right (right-twist barrel) in a steady-state angle due to the spin of the bullet. This angle is small compared to the epicyclic motion, though it's responsible for the drift. The reason for the yaw of repose is explained in detail in chap. 10.6.

 

[bronco9588]

Re: Windage Effects

Yea... I think we may never know what McCoy used for the example problem 9.1. I ended up splurging on Carlucci to see if he includes more information on the 6 DOF calculations. Thanks for clearing up the confusion. Maybe Bryan may weigh in on this 'cause I am sure that he has done the academic exercise.

1) Cn_pa?
2) How do we translate unit vector axis (x vector) with the time step? Is it simply x2 = x1 + dxdt1*dt? I feel like that equation would not apply for the "rotation" of a vector, since it is the "translation" of a point. I think the units of dxdt are rad/sec.

Just another day in paradise...

 

[Killer Spade 13]

Re: Windage Effects (Ballistic Calculations)

OK, let the flames begin.

It's my <span style="font-size: 11pt"><span style="font-weight: bold">OPINION</span></span> that unless you are in an open expanse with a given and known weather front moving through at a certain, speed, the wind, at best, is a SWAG (Scientific Wild Ass Guess).

There is no way to calculate what the wind is doing, or is going to do at every 100 or 200 meter increment out to a 1000 meter or longer shot. You just sort of eyeball it and go for broke.

Like they say, "Only pigs can see the wind."

 

[bronco9588]

Re: Windage Effects (Ballistic Calculations)

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: Killer Spade 13</div><div class="ubbcode-body">OK, let the flames begin.

It's my <span style="font-size: 11pt"><span style="font-weight: bold">OPINION</span></span> that unless you are in an open expanse with a given and known weather front moving through at a certain, speed, the wind, at best, is a SWAG (Scientific Wild Ass Guess).

There is no way to calculate what the wind is doing, or is going to do at every 100 or 200 meter increment out to a 1000 meter or longer shot. You just sort of eyeball it and go for broke.

Like they say, "Only pigs can see the wind." </div></div>

You have somewhat a point, but never say never... I would refer you to DARPAs ONESHOT and Racer's Edge laser anemometers utilized by America's Cup boats to get both magnitude and direction at up to 300 meters. The technology has a ways to go, but IMO will be affordable in a decade or so. LIDAR anemometers have been in use at weather stations to get wind velocities, and various heights, but are too massive for the sniper team or the recreational shooter.

However, the comment is slightly off of discussion, as I am trying to replicate a 6 DOF model calculation, and several steps past "Windage Effects." I do acknowledge that the thread topic is slightly misleading and tried to clear confusion with "(Ballistic Calculations)." You do bring up a very good point that windage is the big non determinant here. It takes a lifetime to master wind estimates and shooters develop more of an art of wind reading rather than a science.

 

[Bearwalk]

Re: Windage Effects (Ballistic Calculations)

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: Killer Spade 13</div><div class="ubbcode-body">OK, let the flames begin.

It's my <span style="font-size: 11pt"><span style="font-weight: bold">OPINION</span></span> that unless you are in an open expanse with a given and known weather front moving through at a certain, speed, the wind, at best, is a SWAG (Scientific Wild Ass Guess).

There is no way to calculate what the wind is doing, or is going to do at every 100 or 200 meter increment out to a 1000 meter or longer shot. You just sort of eyeball it and go for broke.

Like they say, "Only pigs can see the wind." </div></div>


There is a good wind thread going on over in Basic Marksnmanship which is probably a better fit for where you want to go with the discussion.