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enter image description hereWhen computing the takeoff distance on a grassy runway with a 9-knot headwind, should I first do the calculations for the grassy runway (note no. 5) on my ground roll, then apply the wind corrections (note no. 4), or vice versa?

Can I have a solution from this example? Note: values are not based from the attached table

  1. Ground roll: 1000 feet
  2. Total distance to clear 50 feet: 1200 feet
  3. Wind: 9 knots Headwind
  4. Runway: Grassy

Thank you, Captains.

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I'll work with a 10kt headwind, so I can simply use the 10% decrease.

If $X$ is the ground roll, you might think that 'decrease distance by 10%' means:

$X - 0.1 \, X$

And you would be correct. However, you can also write this as (pull the $X$ out):

$(1-0.1)\, X$

or (and simplify)

$0.9 \, X$

Similarly, a 15% increase could be interpreted as:

$X + 0.15 \, X$

or

$1.15 \, X$

So, if we need to do both, I would assume that the factors need to be applied 'on top of' each other -- not based on the original ground roll. Consequently, it doesn't matter which order we apply them...

$0.9 \times 1.15 \, X$

or

$1.15 \times 0.9 \, X$

or

$1.035 \, X$

Working with the multiplication version of each statement is easier -- in that it makes the order independence more obvious.

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  • $\begingroup$ I appreciate your reply, sir! For the ground roll, either way will work but the problem will occur during the computation for total distance to clear 50 feet. It says the "ground roll figure" only. Im confused whether to calculate for wind (variable factor) first or the grassy runway (constant factor). $\endgroup$
    – AerospaceX
    Commented Aug 7 at 11:50
  • $\begingroup$ Example. 1. Compute for headwind first For ground roll: • 1000 x 0.10 = 100, 1000-100 = 900 feet new ground roll • 900 x 0.15 = 135 feet (15% of ground roll figure) • 900 + 135 = 1035 feet final ground roll. For distancce to clear 50 feet: • 1200 + 135 (15% of ground roll figure) = 1335 new distance to clear 50 feet • 1335 x 0.10 = 133.5, 1335 - 133.5 = 1201.5 feet final distance to clear 50 feet $\endgroup$
    – AerospaceX
    Commented Aug 7 at 11:50
  • $\begingroup$ 2. Compute grassy runway first: For ground roll: • 1000 x 0.15 = 150 (15% of the ground roll figure) • 1000 + 150 = 1150 new ground roll • 1150 x 0.10 = 115, 1150-115 = 1035 final ground roll For distance to clear 50 feet: • 1200 + 150 (15% of the ground roll figure) = 1350 feet new distance to clear 50 feet • 1350 feet x 0.10 = 135, 1350 - 135 = 1215 feet final distance to clear 50 feet $\endgroup$
    – AerospaceX
    Commented Aug 7 at 11:52
  • $\begingroup$ Based from the 2 computations, the answers for distance to clear 50 feet are not the same unlike for the "final ground roll". $\endgroup$
    – AerospaceX
    Commented Aug 7 at 11:53
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    $\begingroup$ I would apply the headwind first (it applies to both the ground roll and the climb segment). After headwind, you have 900 ft. ground roll and 1080ft total to 50'. 15% of 900 is 135, so add that to both numbers to take grass into account. 1035 ground roll, 1215 total to 50'. That said, I have a friend who perished in a small light aircraft when they took off heavy, uphill, on a grass strip, flaps down, with a light tailwind (NTSB ATL05FA098). So, I might be tempted to apply the 15% to the un-modified 1000 ft. in an abundance of caution. 1200*0.9+0.15*1000=1230ft. $\endgroup$
    – Rob McDonald
    Commented Aug 7 at 17:35

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