Column 12 is headed “Change of range for variation in density of air of -10 percent.” For use under conditions where no aloft observations of air density are possible, a table has been prepared based on the results of many past observations aloft. The entering arguments are the height of the maximum ordinate in feet and the surface density; the result is the ballistic density. Standard surface density has been arbitrarily selected as the density of the atmosphere which results from a temperature of 59° F., a barometric pressure of 29.53 inches of mercury, and a humidity of 78 percent saturation. This standard surface density is assigned a numerical value of 1.000. To determine the variation in the trajectory caused by variation from standard surface density, the temperature and barometric pressure are measured at the surface and the resulting density is expressed as a percentage of the standard. (Variations from standard percentage of saturation are neglected.) This percentage of standard density at the surface is then used as an entering argument to the table of ballistic density (not shown in the appendix) and from it the ballistic density is found.
The minus sign in the heading of column 12 indicates that a reduction in air density causes an increase in range, the plus sign in the column being understood. Conversely, an increase in air density causes a decrease in range. In order to use the table for a given ballistic density, it is necessary to compare the percentage variations from standard with the 10-percent variation from standard on which the column is based.
Example: Given ballistic density of 1.059, find from column 12 the range error resulting from the non-standard atmosphere, for the 5”/38 caliber, 2,500-foot-second gun, firing at a range of 10,000 yards.
Solution: The percentage variation from standard is l.059-1.000=(+) 0.059= (+) 5.9 percent. The value in column 12 is based on a (-) 10-percent variation from standard. The value taken from the column must, therefore, have a minus sign and the error is 5.9/10 X (-) 501 = -296 yards, or 296 yards short.
Note that the correction to compensate for this error in range is ADD 296 YARDS.
17B7. Use of the nomogram
An alternate means of determining the change of range for variation of air density is by nomogram. The nomogram provided with the 5”/38 caliber range table (appendix C, Part. 1) is an example of the type in use in the fleet today. When aloft aerological observations are not available, it gives a rapid solution of the error in range due to variation in atmospheric density.
Instructions for its use are provided with the nomogram.
Example: Find the error in range for the 5”/38 caliber 2,500-foot-second gun, firing at range 10,000 yards, due to surface air temperature at 40 degrees F. and surface barometric pressure of 30.10 inches of mercury.
Solution: Alignment of 40° and 30.10” provides a point on the support line of the nomogram, which is the equivalent of determining the surface density. Alignment of that point with 10,000 on scale R gives an error in range of -280 yards. The necessary correction is, therefore, ADD 280 YARDS.
The use of the nomogram is more accurate than results obtained from using column 12 with surface observations, as it takes into account the ratio between mean measured and standard density for the actual maximum ordinate obtained.
NOTE: Some recent range tables, including the one reproduced in appendix C, have an additional column, 12a, which gives the change of range for a variation of temperature of the air of -10° F. from the standard air temperature. The effect given in column 12a is that caused by change in the elasticity of the air and is independent of and additional to the effect of any change in density. Column 12a is used with surface air temperature; the standard being taken as 59 degrees F.