This article is an addition to and continuation of the method of using density altitude in computing ballistic performance, Making Ballistic Cards Using Density Altitude
Your Kestrel includes humidity in its calculation of density altitude. This method does not. However, it will get you pretty close if you don't have a Kestrel or other weather meter to do the calculation for you.
First we must calculate the pressure altitude, because barometric pressure varies, which affects the pressure altitude. The pressure altitude is the altitude an aircraft altimeter would read at our location if the reference pressure on the altimeter were set to the current sea-level barometric pressure.
Then we must compensate the pressure altitude for the temperature, which is usually different than the ICAO standard temperature at the pressure altitude.
Step 1 Calculation of Pressure Altitude
If you have the station pressure, from a watch or other instrument, we can use this formula:
If we know the sea-level barometric pressure, we can do one of two things.
But what if we have nothing to tell us the atmospheric pressure at all? Then do this:
Step 2 Correction for Temperature
Now, using the example for pressure altitude of 7,420 feet with a temperature of 78 degrees F., we have to correct that for the difference between the ICAO temperature and the actual temperature. Why do we have to do that? Hotter air is less dense than cooler air, so, if the air temperature is warmer than the ISA temperature at our altitude, the density altitude will be correspondingly higher.
Step 2a - Calculation of ISA Temperature at Pressure Altitude
Step 2b - Calculation of Temperature Correction in Feet
Step 3 Add Pressure Altitude and Temperature Correction
Density Altitude = Pressure Altitude + Temperature Correction.The increase from the temperature correction results from the fact that the temperature is above the ISA temperature for that altitude. If the temperature were below the ISA Temperature, the correction would be negative, and the Density Altitude would be lower than the pressure altitude.
Or, you can use this chart to do the temperature correction. Use the Pressure Altitude obtained from Step 1.
Chart Courtesy of Michael Field
How Accurate is this Calculation?
If we put the data from the calculation above into the Density Altitude calculator here this is what we get:
So, the error is not very large.
It's not as accurate as the calculation of density altitude from a Kestrel or other weather meter.
The calculation neglects humidity - but we know that humidity is a minor factor in shooting at distances out to about 1000 yards with most small arms capable of shooting to that distance with some accuracy.
If we are not using the station pressure to calculate the pressure altitude, we are also an making an assumption that the decline of barometric pressure with altitude is linear and about one inch of mercury per thousand feet. That isn't true at higher altitudes.
So, it's not perfectly accurate at longer distances at higher altitudes. The conclusion we might reasonably draw from that is, if you're going to use a Density Altitude Table for shooting long distances under differing environmental conditions, a Kestrel or other weather meter which calculates density altitude would be a useful piece of kit.
A method which gets us close to the correct answer is better than no answer at all.
Note 1: A precise formula for pressure altitude as a function of station pressure is here. I don't recommend it for manual calculation, unless you have access to a scientific calculator. If you're going to haul around a scientific calculator in the field, you might just as well haul a PDA with an installed ballistic program.