200 mph
without drag 2692 m
with drag 2387 m

   x   y   z   t   v   vx   vy   vz
0   0,00   0,00   5059,680   0,000   89,408   88,050   0,000   -15,526
1   200,00   0,00   4998,807   2,292   94,227   86,438   0,000   -37,513
2   400,00   0,00   4885,409   4,629   103,463   84,688   0,000   -59,436
3   600,00   0,00   4717,281   7,018   115,917   82,721   0,000   -81,203
4   800,00   0,00   4491,775   9,469   130,467   80,473   0,000   -102,692
5   1000,00   0,00   4205,627   11,994   146,228   77,893   0,000   -123,754
6   1200,00   0,00   3854,735   14,610   162,521   74,936   0,000   -144,214
7   1400,00   0,00   3433,860   17,340   178,802   71,558   0,000   -163,859
8   1600,00   0,00   2936,196   20,211   194,594   67,713   0,000   -182,433
9   1800,00   0,00   2352,714   23,262   209,427   63,355   0,000   -199,615
10   2000,00   0,00   1671,090   26,546   222,788   58,425   0,000   -214,990
11   2200,00   0,00   873,873   30,139   234,058   52,859   0,000   -228,011
12   2400,00   0,00   -64,949   34,162   242,440   46,577   0,000   -237,923

And if the engine does not deforms hitting the ground, it could travel as much as 16 m in the soil!
(based on a very naive estimation).

Jan,
working in the metric system has many advantages, so I did convert everything to that system first (see the Excel spreadsheet that was included in the previous post):
                              
               convert to metric         velocity components         
height dropped      16600   ft   5059,68   m         vx=   105,6596299   m/s   
velocity dropped      240   mph   107,2896   m/s         vz=   -18,63064352   m/s   
angle      -10   degrees   -0,174532925   rad                  

Then without air drag one can almost compute the distance where the engine hits the ground without any computers ... if one rounds off the numbers t^2=5000 *2 /10=1000, t=32s. Distance travelled=32*100=3200m
The 10 degrees is taken in account (vx vz), but that does not changes the impact zone much.

More accurately, but still for the case of no airdrag, one has to solve an equation like                            
z(t)=5059-18,6*t-0,5*9,81*t2   

if you do that then                           
                                 
Z(t)      z   -5,50723E-06   m   t   30,27447353   s            
                                 
x(t)   3198,789668   m                           

What about air drag?
I have made an estimate of what the ballistic coefficient (measure of drag) could be, put it into the computer program and got the table. I changed the values of the coefficient and looked at their effect. Then, convinced, I fixed the coefficient and presented the results in the previous post.

This is the educated guess, there could be some more drag, but there has to be a lot of drag before the engine hits the ground at 2km. If the motor started spinning then this might be the case. However, I think that it is very likely that you find the motor at 2,5-3 km.

Where was the motor lost?

Jan, after some thoughts, it isn't too difficult.

You made an error in your calculations. The better formula for the height as function of time : z(t)  =  z0-vz*t-0,5*9,81*t^2
vx=106 m/s
vz=18,6 m/s

In absence of air resistance the engine falls 30,2 s and travels 3198 m

With air resistance ... I made the following calculation ...
the engine falls about 34 s and travels about 2820 m

(It was done by a computer program that is not downloadable)

included a spreadsheet with the calculations


Robert

   m   m   m   s   m   m/s   m/s   m/s
   x   y   z   t   v   vx   vy   vz
0   0   0   5059,68   0   107,2896   105,6596299   0   -18,63064352
1   200   0   5006,632916   1,91011851   110,0991639   103,7476291   0   -36,85451598
2   400   0   4917,130465   3,856500547   115,684911   101,7493745   0   -55,04601183
3   600   0   4789,722193   5,842786049   123,5918684   99,61176624   0   -73,16041258
4   800   0   4622,758705   7,874016067   133,3068689   97,28770152   0   -91,13629582
5   1000   0   4414,321708   9,956771129   144,3379402   94,73571952   0   -108,8971277
6   1200   0   4162,139533   12,09939126   156,2491124   91,91865116   0   -126,3516787
7   1400   0   3863,480602   14,31232618   168,6631164   88,80195378   0   -143,3926771
8   1600   0   3515,013049   16,60867491   181,2484026   85,35206006   0   -159,8937437
9   1800   0   3112,612007   19,00500448   193,7007394   81,53484683   0   -175,7044257
10   2000   0   2651,084582   21,5225951   205,7235961   77,31419936   0   -190,6428928
11   2200   0   2123,761651   24,18937213   217,0078103   72,65058728   0   -204,4854075
12   2400   0   1521,865416   27,04300366   227,2089519   67,49953732   0   -216,9509629
13   2600   0   833,4792567   30,13609712   235,919091   61,80985336   0   -227,6781929
14   2800   0   41,76410461   33,54545389   242,6270797   55,52136465   0   -236,1890723

Jan,

interesting question, could be a question of my father too! I think I can make an educated guess and produce a spreadsheet for you.

However, I have first to pounder about the issue - what is the drag of an motor, and then make some calculations. This costs me about one or two weeks - I have so many other things to do - but I will do it.

It would greatly help if you have some data from similcar cases, even bomb trajectories.

Robert

I have updated most of the downloads,

• BfX.xll includes now BfX_Cd that allows you to extract the drag function values that BfX uses
• The previous drag function RA contained in BfX overestimated the drag around the speed of sound and has been replaced
• BfX_I interpolates smarter and is able to show some additional information how accurate and how the results are interpolated

See the GettingStarted workbook for explanations

Furthermore, most workbooks are somewhat improved

Users of BfX,

Beginning of may I will release an update of BfX.

I worked a bit on BfX_I so that it can cope with more situations. The function also yield info on the quality of each interpolation.

I improved the implementation of the RA4 (small bore, .22LR) drag function. Due to an error, the one currently in use has to much drag arround the sound velocity.

Another function was added to BfX that yields the drag coeficient (drag function) as a function of bullet velocity for G1, G2.... One use for this is that BfX drag coeficients can be checked with others.

Some Excel filles in the download section will be updated to reflect the new functionality.

Robert

Paul,
any progress?

Robert

I you don't succeed I'll do it for you.

and if you know the muzzle velocity then you can remove it from solver.

Ja,

I provided a worksheet that is doing exactly that already - calculating from velocity and distances a bc. Look at the download page at

"Show me how Solver can be used with BfX VBA?"

However, a much simpler version is attached to the post.


Robert

I have tried that, but after some experiments (including some dedicated interfaces in bfx.xll) I got stuck.  It is certainly possible and I have to say that I spend not too much time on this.

It is quite easy for me to add another set of interfaces to bfx.xll to support vb.net, however I was looking for some general purpose data types like variants (or the xltype of Excel) for easy usage and to have the flexibility of using optional arguments i.e. to support a vb call like v=bfx_vx(700, 30, 0.5) and v=bfx_vx(700, 30, "yd", 0,5). So after some trying I paused my developments there. Furthermore array passing and accessing should be friendly for the programmer. bfx.xll runs in an unmanaged environment, not int the .net engine - adding additional levels of complexity.

If you know a receipy for this then I am quite willing to implement such interfaces.

Robert

Well,

the forum is online again. See if we are less popular for persons who want to sell things.

Robert

The forum is finally online!

After years of more less then more working at the physics and software of BfX.xll - the Excel 2003 and 2007 addin - and a month or so on the website and forum, I decided to put it all online. My main motivation for providing the BfX.xll is that I thought that the software is as useful to fellow match shooters as it turned out for myself. BfX is great for the calculations of sight settings and in the analysis of the effects of wind.

Do not hesistate to post, although I realy do not know what to expect!

Robert