Part I:  Find the remaining velocity/time of flight

A compilation of Ingall's ballistic table:

   1      2        3         4         5
       
  100  63695.4   867.09    199.20    7.120       
  150  55024.5   615.21    127.92    3.570       
  200  48872.4   477.19     92.27    2.140       
  250  44100.5   389.86     70.89    1.430       
  300  40201.6   329.65     56.63    1.010       
  350  36905.1   285.56     46.45    0.760       
  400  34049.5   251.88     38.81    0.590       
  450  31530.7   225.31     32.87    0.480       The following variables will
  500  29277.6   203.82     28.12    0.390	     be used throughout:
  550  27239.4   186.07     24.23    0.320        
  600  25378.7   171.18     20.99    0.270       Column 1: Velocity 'v'
  650  23666.9   158.47     18.25    0.240       Column 2: Space function 'sf'
  700  22082.2   147.55     16.71    0.210       Column 3: Space function     
  750  20606.7   137.76     13.86    0.180                 change 'sd'        
  800  19229.1   123.89     12.08    0.150       Column 4: Time function 'tf' 
  850  17990.2   110.12     10.58    0.130       Column 5: Time function      
  900  16889.0    98.53      9.32    0.110                 change 'td'        
  950  15903.7    86.90      8.25    0.090                                    
 1000  15034.7    71.60      7.36    0.070       Initial Velocity 'V'         
 1050  14318.5    59.19      6.66    0.060       Range in feet 'r'
 1100  13726.6    49.34      6.11    0.040       Ballistic Coefficient 'b'
 1150  13233.2    41.46      5.67    0.040
 1200  12818.6    35.33      5.32    0.030
 1250  12465.3    32.15      5.03    0.030
 1300  12143.8    29.77      4.78    0.023
 1350  11846.1    27.76      4.55    0.020
 1400  11568.5    26.65      4.35    0.018
 1450  11302.0    25.78      4.17    0.018
 1500  11044.2    24.91      3.99    0.016
 1550  10795.1    24.13      3.83    0.016
 1600  10553.8    23.38      3.67    0.014
 1650  10320.0    22.69      3.53    0.013
 1700  10093.1    22.02      3.40    0.013
 1750   9872.9    21.41      3.27    0.012
 1800   9658.8    20.89      3.15    0.012
 1850   9449.9    20.49      3.03    0.011
 1900   9245.0    20.13      2.92    0.010
 1950   9043.7    19.76      2.82    0.011
 2000   8846.1    19.42      2.71    0.009
 2050   8651.9    19.10      2.62    0.009
 2100   8460.9    18.70      2.53    0.009
 2150   8273.2    18.48      2.44    0.008
 2200   8088.4    18.18      2.36    0.008
 2250   7906.6    17.90      2.28    0.008
 2300   7727.6    17.63      2.20    0.008
 2350   7551.3    17.37      2.12    0.007
 2400   7377.6    17.12      2.05    0.007
 2450   7206.4    16.88      1.98    0.007
 2500   7037.6    16.64      1.91    0.007
 2550   6871.2    16.41      1.84    0.006
 2600   6707.1    16.20      1.78    0.006
 2650   6545.1    16.08      1.72    0.006
 2700   6384.8    15.87      1.66    0.006
 2750   6226.1    15.70      1.60    0.006
 2800   6069.1    15.56      1.54    0.005
 2850   5913.5    15.41      1.49    0.005
 2900   5759.4    15.26      1.44    0.005
 2950   5606.8    15.11      1.38    0.005
 3000   5455.7    14.98      1.33    0.005
 3050   5305.9    14.85      1.28    0.005
 3100   5157.4    14.71      1.23    0.005
 3150   5010.3    14.59      1.19    0.005
 3200   4864.4    14.46      1.14    0.005
 3250   4719.8    14.34      1.10    0.004
 3300   4576.4    14.23      1.05    0.005
 3350   4534.1    14.10      1.01    0.004
 3400   4293.1    13.99      0.97    0.004
 3450   4153.2    13.88      0.93    0.004
 3500   4014.4    13.77      0.89    0.004
 3550   3876.7    13.67      0.85    0.004
 3600   3740.0    13.56      0.81    0.004
 3650   3604.4    13.46      0.77    0.004
 3700   3469.8    13.36      0.74    0.003
 3750   3336.2    13.26      0.70    0.004
 3800   3203.6    13.17      0.66    0.004
 3850   3071.9    13.07      0.63    0.003
 3900   2941.2    12.99      0.60    0.003
 3950   2811.3    12.88      0.56    0.003
 4000   2682.5    12.80      0.53    0.003
 4050   2599.5    12.72      0.50    0.003
 4100   2427.3    12.62      0.47    0.003
 4150   2301.1    12.56      0.44    0.003
 4200   2175.5    12.47      0.41    0.003
 4250   2050.8    12.38      0.38    0.003
 4300   1927.0    12.31      0.35    0.003
 4350   1803.9    12.23      0.32    0.003
 4400   1681.6    12.15      0.29    0.003
 4450   1560.1    12.08      0.26    0.003
 4500   1439.3    12.01      0.24    0.002
 4550   1319.2    11.93      0.21    0.003
 4600   1199.9    11.86      0.19    0.002
 4650   1081.3    11.79      0.16    0.003
 4700    963.4    11.72      0.13    0.002
 4750    846.2    11.65      0.11    0.002
 4800    729.7    11.59      0.09    0.003
 4850    613.8    11.52      0.06    0.003
 4900    498.6    11.47      0.09    0.003
 4950    383.9    11.39      0.01    0.002

	Examples will be based on a projectile weighing 170 grains with
a ballistic coefficient of .44 leaving the muzzle of a firearm at 3225 feet
per second.

===== Remaining Velocity:  
(Note - formula line is cumulative)

	Step 1:  Find the nearest lower velocity to the muzzle, or
                 beginning, velocity.

		 Formula: V-v
		 
                 3225-3200 = 25

	Step 2:  Divide this number by 5 and multiply the answer by the 
                 number in Column 3 of the chart at that row.

		 Formula: ((V-v)/5) x sd

		 25/5 = 5
		 5 x 14.46 = 72.3

	Step 3:  Subtract this number from the number found in Column 
		 2 of the table at the same row.

		 Formula: (((V-v)/5) x sd)) - sf

		 4864.4 - 72.3 = 4612.1

	Step 4:  Add this to the range in feet divided by the ballistic
		 coefficient.

		 Formula: (((V-v)/5) x sd) + sf + r/b = rs
                          ('rs' is the remaining space function)

		 4612.1 + 300/.44 = 5618.5

	Step 5:  Find the nearest higher number in Column 2 of the chart to
		 this and subtract it out.

		 Formula: rs-sf
                                          
		  5305.9 - 5293.9 = 12

	Step 6:  Divide this result by the number in Column 3 and multiply
		 by 5.

		 Formula: ((rs-sf)/sd) x 5

		 (12/14.85) x 5 = 4.04


	Step 7:  Add this to the number in Column 1; the 
		 result is the remaining velocity.

		 Formula: (((rs-sf)/sd) x 5) + v = Remaining velocity

		 4.04 + 3050 = 3054.04

Time of Flight:

	Step 1:  Find the nearest lower velocity to the beginning velocity
		 and subtract it from the beginning velocity.  Divide
		 this number by 5.

		 Formula: (V-v)/5

                 (3225-3200)/5 = 5

	Step 2:  Multiply this answer by the number found in Column 5 on
                 the same row, and add Column 4.

		 Formula: (((V-v)/5) x td) + tf = ts

		 (5 x .005) + 1.14 = 1.165
			             (Note - 'ts' is the start time)

	Step 3:  Repeat steps 1 and 2 for the remaining velocity.

		 Formula: (((V-v)/5) x td) + tf = te

		 (((3054.04-3050)/5) x .005) + 1.28 = 1.284
					              (Note - this is 'te')

	Step 4:  Subtract the start time from the end time.

		 Formula: te - ts = time of flight

		 1.284 - 1.165 = .11 seconds



===== Drop from the line of bore:

  1     2
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  1   193
 .98   192            The following variables will be used throughout:
 .96   191            
 .94   190            Column 1:  Percentage of remaining velocity 
 .92   187	      Column 2:  Drop function  'df'
 .90   186
 .88   185   	      Beginning velocity 'V'
 .86   184            Remaining velocity 'v'
 .84   182	      Time of flight 't'
 .82   181
 .80   180
 .78   178
 .76   176
 .74   175
 .72   174
 .70   172
 .68   170
 .66   169
 .64   167
 .62   166
 .60   164
 .58   162
 .56   162
 .54   160
 .52   157
 .5    156
 .48   154
 .46   152
 .44   150
 .40   145
 .38   144
 .36   142
 .34   139
 .32   137

	Step 1:  Find the percentage of velocity remaining.

		 Formula:  v/V

		 3055.04/3225 = .947

	Step 2:  Multiply the time of flight squared by the number found
		 in column 2 corresponding to the percentage of velocity
		 left in Column 1.  Some rounding may be required.

                                 2
		 Formula:  df x t

		 (.11 x .11) x 190 = 2.3 inches

Note: This is not the drop from the line of sight, only from the line of
      bore.  See the file balli.txt to calculate the trajectory path from
      this information.
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