Title: **How to calculate Cd**

Post by:**375CT** on **September 22, 2014, 08:31:54 PM**

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Folks, I wonder if someone has the equations to compute Cd (coeff of drag) from observed downrange velocities.

I know how to do that with BCs, now I'd like to know how to do the same for Cd. Any help is much appreciated in advance. :)

I know how to do that with BCs, now I'd like to know how to do the same for Cd. Any help is much appreciated in advance. :)

Title: **Re: How to calculate Cd**

Post by:**meccastreisand** on **September 22, 2014, 10:23:23 PM**

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I think I have basically what you're looking for buried in some hidden tabs on my Ballistic_XLR workbook.

you can download it at Ballisticxlr.com. If you need detailed info on it you can get in touch with me there too.

you can download it at Ballisticxlr.com. If you need detailed info on it you can get in touch with me there too.

Title: **Re: How to calculate Cd**

Post by:**375CT** on **September 23, 2014, 08:37:13 AM**

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Quote from: meccastreisand on September 22, 2014, 10:23:23 PM

I think I have basically what you're looking for buried in some hidden tabs on my Ballistic_XLR workbook.

you can download it at Ballisticxlr.com. If you need detailed info on it you can get in touch with me there too.

For some reason I cannot download your workbook. Google raised an error message, so please can you check?

So, you say that from downrange velocities, you can calculate Cd (for any G function) ? Am I right?

Thanks in advance for any help!

Title: **Re: How to calculate Cd**

Post by:**admin** on **September 23, 2014, 01:21:22 PM**

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I think I have missed this request.

On my downloads page you can download a workbook, here a screen copy.

http://www.bfxyz.nl/pics/bcfromvelocitysimplelarge.PNG (http://www.bfxyz.nl/pics/bcfromvelocitysimplelarge.PNG)

It uses velocity measurements at several distances, yet one can apply the same method to a single measurement.

Yet the more measurements (at the same or different disatances) the better the results/

Alternatively you might post your data and I reply with an excel document that does the job.

On my downloads page you can download a workbook, here a screen copy.

http://www.bfxyz.nl/pics/bcfromvelocitysimplelarge.PNG (http://www.bfxyz.nl/pics/bcfromvelocitysimplelarge.PNG)

It uses velocity measurements at several distances, yet one can apply the same method to a single measurement.

Yet the more measurements (at the same or different disatances) the better the results/

Alternatively you might post your data and I reply with an excel document that does the job.

Title: **Re: How to calculate Cd**

Post by:**375CT** on **September 23, 2014, 09:13:23 PM**

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Quote from: admin on September 23, 2014, 01:21:22 PM

I think I have missed this request.

On my downloads page you can download a workbook, here a screen copy.

http://www.bfxyz.nl/pics/bcfromvelocitysimplelarge.PNG (http://www.bfxyz.nl/pics/bcfromvelocitysimplelarge.PNG)

It uses velocity measurements at several distances, yet one can apply the same method to a single measurement.

Yet the more measurements (at the same or different disatances) the better the results/

Alternatively you might post your data and I reply with an excel document that does the job.

Robert, thanks for the graph. I don't have any measurements yet, but if you can tell me how to do the spreadsheet I can try. Any help, much apprecitated for sure!

Title: **Re: How to calculate Cd**

Post by:**meccastreisand** on **September 24, 2014, 11:49:10 PM**

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Quote from: 375CT on September 23, 2014, 08:37:13 AMWhen you click on the excel file at the download share it'll show you an image of the spreadsheet. At the top will be an open link and an arrow pointing downward that will download it for you.Quote from: meccastreisand on September 22, 2014, 10:23:23 PM

I think I have basically what you're looking for buried in some hidden tabs on my Ballistic_XLR workbook.

you can download it at Ballisticxlr.com. If you need detailed info on it you can get in touch with me there too.

For some reason I cannot download your workbook. Google raised an error message, so please can you check?

So, you say that from downrange velocities, you can calculate Cd (for any G function) ? Am I right?

Thanks in advance for any help!

Title: **Re: How to calculate Cd**

Post by:**375CT** on **September 26, 2014, 05:00:43 AM**

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Quote from: meccastreisand on September 24, 2014, 11:49:10 PM

When you click on the excel file at the download share it'll show you an image of the spreadsheet. At the top will be an open link and an arrow pointing downward that will download it for you.

Thanks, I finally got it downloaded, but I've revised it and haven't found where Cd is calculated. Please could you tell what tab is or where I should look in?

Title: **Re: How to calculate Cd**

Post by:**meccastreisand** on **October 02, 2014, 05:10:03 PM**

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There are 30 or so hidden tabs that have all the calculations. Find Ballistics Table 0

Title: **Re: How to calculate Cd**

Post by:**375CT** on **October 06, 2014, 07:00:50 AM**

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Quote from: meccastreisand on October 02, 2014, 05:10:03 PM

There are 30 or so hidden tabs that have all the calculations. Find Ballistics Table 0

Thanks a lot for your help. I did what you say but still I cannot find where the Cd are derived from velocities readings. Somewhere else to look at?

Title: **Re: How to calculate Cd**

Post by:**meccastreisand** on **October 15, 2014, 04:40:54 PM**

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unhide Ballistics Table 0 and find cell A23.

Title: **Re: How to calculate Cd**

Post by:**375CT** on **October 18, 2014, 05:57:18 AM**

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Quote from: meccastreisand on October 15, 2014, 04:40:54 PM

unhide Ballistics Table 0 and find cell A23.

Did that, but that cell is for BC adjustments for non-std conditions. Still no luck! :(

Title: **Re: How to calculate Cd**

Post by:**mman** on **November 12, 2014, 05:59:51 AM**

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375CT,

I've been away for long time but if you haven't found a solution yet I have a suggestion. First just use Robert's spreadsheets to calculate BC from velocity measurements. Then use BC drag tables to find out Cd for velocity in question. As you know Cd for bullet is highly velocity depended and it doesn't make sense to calculate single average value for whole supersonic velocity range.

I've been away for long time but if you haven't found a solution yet I have a suggestion. First just use Robert's spreadsheets to calculate BC from velocity measurements. Then use BC drag tables to find out Cd for velocity in question. As you know Cd for bullet is highly velocity depended and it doesn't make sense to calculate single average value for whole supersonic velocity range.

Title: **Re: How to calculate Cd**

Post by:**375CT** on **November 25, 2014, 06:02:50 AM**

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Quote from: mman on November 12, 2014, 05:59:51 AM

375CT,

I've been away for long time but if you haven't found a solution yet I have a suggestion. First just use Robert's spreadsheets to calculate BC from velocity measurements. Then use BC drag tables to find out Cd for velocity in question. As you know Cd for bullet is highly velocity depended and it doesn't make sense to calculate single average value for whole supersonic velocity range.

Mman,

Thanks for the tip, but please could you elaborate a little more over the "use BC drag tables" ? Perhaps I'm missing something here and a small example will help me out. Thanks as usual for your help!

Title: **Re: How to calculate Cd**

Post by:**mman** on **November 28, 2014, 06:30:55 PM**

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Example:

Step 1

You have a bullet with known G7 BC of 0,261. It's 0.264" and 123 grains. Now you can calculate form factor (i7) for it. i7 = weight/7000/(caliber^2*BC) --> i7 = 123/7000 / (0.264^2 * 0,261) = 0,966. This means that bullet's drag is 96,6 % of G7 projectile drag.

Step 2

You can use G7 drag data table to find out Cd for velocity in question (for G7 projectile). See picture below how to do it using G7 graph.

Or using robert's BFx function in excel =BfX_Cd(900;"G7") this gives you 0,262 as a Cd.

Step 3

Since you know that for your bullet drag is 96,6 % of G7 projectile you can calculate for the bullet in question that CD(900m/s) = 0,966* 0,262 = 0,253

Clear enough?

(http://i.imgur.com/NAfV5H7.png)

Now if you are measuring some odd shape bullet that doesn't fit very well to any know drag data (G1, G5, G6, G7 etc..) you can start to work with the closest one and using your measured velocities find out where it goes wrong. Then just do your own custom drag table to modify it as necessary. This is possible since Robert kindly added this option as well. You could use some "best fit" tool to do this but good old trial and error works as well.

Step 1

You have a bullet with known G7 BC of 0,261. It's 0.264" and 123 grains. Now you can calculate form factor (i7) for it. i7 = weight/7000/(caliber^2*BC) --> i7 = 123/7000 / (0.264^2 * 0,261) = 0,966. This means that bullet's drag is 96,6 % of G7 projectile drag.

Step 2

You can use G7 drag data table to find out Cd for velocity in question (for G7 projectile). See picture below how to do it using G7 graph.

Or using robert's BFx function in excel =BfX_Cd(900;"G7") this gives you 0,262 as a Cd.

Step 3

Since you know that for your bullet drag is 96,6 % of G7 projectile you can calculate for the bullet in question that CD(900m/s) = 0,966* 0,262 = 0,253

Clear enough?

(http://i.imgur.com/NAfV5H7.png)

Now if you are measuring some odd shape bullet that doesn't fit very well to any know drag data (G1, G5, G6, G7 etc..) you can start to work with the closest one and using your measured velocities find out where it goes wrong. Then just do your own custom drag table to modify it as necessary. This is possible since Robert kindly added this option as well. You could use some "best fit" tool to do this but good old trial and error works as well.

Title: **Re: How to calculate Cd**

Post by:**375CT** on **January 08, 2015, 05:09:27 AM**

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Mman,

Sorry for the late reply!

While the example you posted is clear enough, my point was/is if you are aware of an analytical approach to solve for Cd given

1) You don't know/have any initial approximate G value.

2) You only have downrange measured velocities.

Or...you always have to start with a BC calc?

Thanks!

Sorry for the late reply!

While the example you posted is clear enough, my point was/is if you are aware of an analytical approach to solve for Cd given

1) You don't know/have any initial approximate G value.

2) You only have downrange measured velocities.

Or...you always have to start with a BC calc?

Thanks!

Title: **Re: How to calculate Cd**

Post by:**mman** on **January 08, 2015, 04:21:25 PM**

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375CT,

There are lot's of analytical and numerical ways to estimate Cd directly. However the method I just told you is one of the most accurate and still very simple.

If you don't know the actual BC of your bullet use measurements and drawings from Litz's book to estimate form factor and calculate BC from it (I have done this numerous times and usually get the BC right with the accuracy of 3-4 % which is better than I can manage with CFD). All you need for this method is good reference bullet. When you have BC then just use G-drag curve as shown before to calculate Cd.

There are lot's of analytical and numerical ways to estimate Cd directly. However the method I just told you is one of the most accurate and still very simple.

If you don't know the actual BC of your bullet use measurements and drawings from Litz's book to estimate form factor and calculate BC from it (I have done this numerous times and usually get the BC right with the accuracy of 3-4 % which is better than I can manage with CFD). All you need for this method is good reference bullet. When you have BC then just use G-drag curve as shown before to calculate Cd.

Title: **Re: How to calculate Cd**

Post by:**375CT** on **January 09, 2015, 03:11:15 AM**

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Quote from: mman on January 08, 2015, 04:21:25 PM

375CT,

There are lot's of analytical and numerical ways to estimate Cd directly. However the method I just told you is one of the most accurate and still very simple.

If you don't know the actual BC of your bullet use measurements and drawings from Litz's book to estimate form factor and calculate BC from it (I have done this numerous times and usually get the BC right with the accuracy of 3-4 % which is better than I can manage with CFD). All you need for this method is good reference bullet. When you have BC then just use G-drag curve as shown before to calculate Cd.

Mman, thanks again for your kind reply.

Are you aware of any other method, besides McDrag to compute Cd?

Title: **Re: How to calculate Cd**

Post by:**mman** on **January 09, 2015, 06:55:29 AM**

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I can't give you direct references I'm afraid but I have seen some of them along the way. For me those are not very interesting since most are not that accurate except perhaps limited projectile shapes.

Let's see if robert can do a better job with his new project.

Let's see if robert can do a better job with his new project.