Beginer needs help with Density altitude questions

[JCH]

Hello I have just begun my training and I have the Gleim 2020 pilot book I'm wanting to understand how to calculate the density altitude by mathematical equation rather than relying on a chart the formula I have seen to be accurate is as follows DA=PA+{120*(OAT- ISA TEMP) } is this formula correct? The Gleim book seems to have very different math that calculates this and being that their answer is pulled from a chart makes it difficult to understand
I can post the exact question from the book if needed
Thanks,
JC

 

[GRG55]

That's the formula.

Here's a bit of amplification:

(A) pressure altitude = (standard pressure - your current pressure setting) x 1,000 + field elevation

(B) density altitude = pressure altitude + [120 x (OAT - ISA Temp)]

(OAT and ISA Temp are in degrees C)



So, for example, my home airport is at 4000 ft ASL. If the current pressure setting was 29.40 and the OAT is 33 deg C then:

pressure altitude = (29.92 - 29.40) x 1000 + 4000
pressure altitude = 4520 ft.

Rule of thumb, decrease ISA temp 2 deg for every 1000 ft above sea level, so at 4000 ft the ISA temp (15 deg C at sea level) will be approximately 15 - 8 = 7 deg C

density altitude = 4520 + [120 x (33 - 7)]
density altitude = 7640 ft.

 

[JCH]

Thank you so much for your detailed answer. From what I have learned I was also using the same calculations to figure pressure altitude and my density altitude. However I got really bent out of shape when I read in the book two answers that were almost the same altitude one was 3010 ft and the other one was 2991 ft. Using my calculation I was closer to the 3010 foot but the conversion chart breaks it out to exactly 2991. I found if I use the same formula and use a correcting factor of 0.948 it corrects the calculation to align with the chart.

pressure altitude = ((29.92 - 29.40) x 0.948) x 1000 + 4000

So is it safe to say that as a general rule Pilots are really concerned with an 18-foot variance in altitude as it is not really that significant and do I need to plan on using this conversion number when I take the written test so I get exactly what they're asking for? Actually almost all of the possible answers there are a lot of feet off this was the only one that had altitude that was such close.

Thanks
JC

 

[denverpilot]

Usually if a chart is provided they want you to use their chart to solve vs the equations. This leads to minor inaccuracies but is more of a test taking skill than a knowledge skill. The test is whether or not you can use the chart more than whether or not you know the formula.