What would be the ground roll and total distance to clear a 50ft obstacle given these conditions?

Question

I'm a student pilot, the question I am trying to answer is

What would be the ground roll and total distance to clear a 50ft obstacle given an elevation of 5,000ft, altimeter 29.52, and a temperature of 25° Celsius, winds calm.

Disclaimer: I'm going to double check with my CFI, obviously, you should too if you are unsure.

So I understand how the chart works, I'm just unclear about the "Elevation 5,000ft. Altimeter at 29.52".

My inclination is to assume that the meaning is sea level pressure is 29.52, and therefore we should adjust our input for "PRESS ALT FT" to be the altitude that reflects that average pressure, which would be 500 feet.

We round up for safety, so assume PRESS ALT=1000' and TEMP=30° Celsius, we would have a ground roll of 890' and a takeoff distance of 1645', right?

Another question: Where do I find the official documentation for converting barometric pressure into the altitude that has that average pressure?

Answer 1

We round up for safety, so assume PRESS ALT=1000' and TEMP=30° Celsius, we would have a ground roll of 890' and a takeoff distance of 1645', right?

Good thinking, but no.

Refer to the Pilot's Handbook of Aeronautical Knowledge, Chapter 10. You want page 10-3 specifically.

When the altimeter setting is 29.92, the pressure altitude is the same as the field elevation. When the altimeter setting changes, you must apply a conversion factor to the field elevation to get pressure altitude.

In this case, the altimeter setting is 29.52, which means that your conversion factor will be about 380 feet:

Therefore, the actual pressure altitude will be 5,380 feet.

If you round up for safety, the takeoff distances will be 1455 and 2855.

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We can get a little more precise than that, though.

To calculate the ground roll at 25 celsius, we can interpolate between 20 and 30 degrees:

5,000 feet

$\left[ \left(1315 - 1215\right) \over 2 \right] + 1215 = 1265$ ground roll at 5000

$\left[ \left(2525 - 2320\right) \over 2 \right] + 2320 = 2422$ 50 ft obstacle at 5000

To correct for pressure altitude, we do the same thing at 6000 feet...

6,000 feet

$\left[ \left(1455 - 1345\right) \over 2 \right] + 1345 = 1400$ ground roll

$\left[ \left(2525 - 2320\right) \over 2 \right] + 2320 = 2732$ 50 ft obstacle

...and then interpolate again:

5,380 feet

$\left[ \left(1400 - 1265\right) * 0.380 \right] + 1265 = 1316$ ground roll

$\left[ \left(2732 - 2422\right) * 0.380 \right] + 2422 = 2540$ 50 ft obstacle