How to find the ISA Temp of a Given Altitude

[Rah.]

I am trying to learn about Density Altitude and in doing so I’ve confused myself. I understand DA= Pressure Altitude +[120x(OAT TEMP-ISA TEMP)]

If there’s an easier/friendlier equation I would appreciate it! Anyways
For example

Using a PA (Pressure Alt) of 2150
The only ISA temp rule of thumb I know is
“Double the altitude, subtract 15 and put a - sign on it” -Nicholas Irving Precision Rifle Bible is where I got that “ROT”

In the book as an example for an ISA TEMP at 10,000Ft multiply by 2 to get 20; then subtract 15 to get 5 and add the -. so DA=5470 + [120 x (35-5)] in this example the DA=9,070

My issue is trying to equate this at a pressure alt of 2150ft with a OAT TEMP of 11° C

So I would assume 2150 x 2 = 4300 so I take 43? - 15 which gives me 28 add the - so -28 in an equation of 2150 + [120 x 11 -28)]. 11-28= -17 x 120 = -2040

-2040+2150= 110 so by my math my density altitude is 110ft which I know cannot be correct if I’m at an actual altitude of 1680ft. Because standard pressure is (29.92) SP* and Current Pressure CP* is at 29.45 to get my Pressure Altitude or PA* I take my standard pressure minus current pressure x 1000 + field elevation of 1680 = 2150.

Where am I going wrong?

 

[_Windrider_]

Don’t over complicate. It’s really simple. Standard atmosphere is 15 degrees C at sea level with a pressure of 29.92 in Hg.

The standard lapse rate is 2 degrees C per 1000 ft increase in altitude/elevation. The standard lapse rate for pressure is 1 in Hg per 1000 feet.

So standard temp and pressure at 5000 feet is 5 C and 24.92 in Hg

 

[Rah.]

So you’re saying at 2500 ft it would be roughly 10 C and 27.42 IN HG? Or am I still screwing the pooch? Thank you for your assistance

 

[_Windrider_]

Yes.

 

[Rah.]

Yes.

Wow. Simple! Thank you so much! Do away with the equations and just do the simple math of knowing it changes 1 in hg per 1000 and 2° C per 1000 from Standards! You’ve solved 3 days of me racking my brain on this equation!

 

[_Windrider_]

in freedom units, it’s 59 degrees F and 29.92 at sea level is standard. Lapse rate is 3.5F per 1000 feet and still 1 inch.
this chart above gets you in the ballpark enough for shooting.

the big takeaway is that about every 15F above standard equals 1000 ft increase in DA. Memorize that and you don’t need this chart.

all this is an approximation and gets you in the shooters ballpark. It ignores pressure effects and humidity. But is close enough for what we do.