Top of Climb Calculation Question

[Ben2k9]

Ok I have the CTLS climbing at about 520fpm and 78kts. I’m trying to figure out distance travelled to get to cruising altitude and I’m not sure if the way I’m doing it is correct. So I’m just taking the 520fpm rate and multiplying that times the altitude climb, and coming up with a time, and then multiplying time x speed to get distance (forget about wind for now). So for 6000 feet of climbing that’s 11.5 minutes, and 11.5 minutes x 78kts is 15nm. 

This is simple enough, but the airspeed would be happening at a diagonal angle, so I’m thinking 15nm distance would not actually be covered across the ground. Am I overthinking this or is there a more precise formula one would use to calculate this?  

[Warmi]

Well, if your 78kts is over the ground then it is already independent from any other variables.

[Ben2k9]

Well if I am going by the airspeed indicator to achieve Vy and I’m aiming for 78 kias, then that is not necessarily ground speed, no?

 

 

[Ed Cesnalis]

you are over thinking it.  

[Ben2k9]

Ok good to know. Got the checkride in a week, and that’s why I’m asking. 

[Warmi]

If it is KIAS then you are talking your distance thru the air at which point you would need to figure out your angle inclination of the triangle  based on your climb rate and then apply Pythagorean theorem to figure out the ground track.  http://mathworld.wolfram.com/PythagoreanTheorem.html which still wouldn't be exact since your KIAS changes as you gain altitude ... or , as Ed says, just enjoy it :-)

BTW .. I never bothered with exact calculations for my check-ride. Just approximate your distance based on some calculated ground speed  - none of that will match exactly anyway ...

[Tom Baker]

I doubt the examiner will want you to go that deep, but if you choose you can just figure the time to climb to altitude at that airspeed, and add a couple minutes at the higher fuel burn for a little safety margin. Anything you do to add a safety margin to your planning the examiner will like.

[FlyingMonkey]

I agree with Tom, asking you to run a Pythagorean Theorem to get the answer is pretty esoteric and a bit beyond the scope of a normal checkride.  The only reason I could imagine needing distance to climb to an altitude would be to clear mountains when departing an airport, but the reality is you could just circle & climb until you were high enough and then proceed on course.