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Under these conditions: Pressure altitude 5,000 ft, Headwind Calm, Temperature 101 F

I have no idea how to even start

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    $\begingroup$ Hi @Matt item 2 is going to be important in your scenario. $\endgroup$ – Mr R May 13 at 20:48
  • $\begingroup$ Yes, read the fine print and apply to 5000 feet, 41F + 60F. If possible, land on a 2000 foot runway, just to be sure. $\endgroup$ – Robert DiGiovanni May 13 at 20:50
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All else being equal, increased temperature increases density altitude, and thus true airspeed for a given indicated/calibrated airspeed. Increased landing speed will increase the landing roll distance.

In your exercise above, the primary relevant condition given is a runway at 5000'. This tells you which column of the table you'll be using, i.e. the one labeled "At 5000 feet & 41 °F". Note that the temperature given there is the "standard" temperature for that altitude.

But there are footnotes. The first footnote, discussing headwind, doesn't apply because there's no headwind. But the second one, discussing temperature does. Your given temperature is 101 °F, which is 60 °F higher than standard temperature for the given altitude of 5000'. The footnote says you need to add 10% to the distance for every 60 °F higher than standard, and there is exactly 60 °F higher temperature given in the conditions, so you need to add 10%.

The standard ground roll is 495', so adding 10% to that you get 544.5' (which you might round to 545').

Note that if the temperature was, for example, only 30 °F higher, that doesn't mean you can ignore the second footnote. You should interpolate based on the information there, adding 5% in that example to the landing roll instead of 10%. Likewise a temperature 90 °F higher would require increasing the landing roll figure by 15% (assuming you think it's even safe to operate the airplane at that temperature! at 131 °F, there are lots of other problems that might argue against flying at all, including failure of paved surfaces, overheating of the engine, pilot dehydration and fatigue, etc.)

You don't say whether the runway is unpaved. The table you're using assumes a "hard surface runway". If it's a grass runway, you'd also want to apply the third footnote. Note that the footnote there is for a "dry, grass runway". A grass runway that's wet, or a gravel runway, or a snowy/icy runway could produce different results. A wet, grass runway in particular could reduce the landing roll significantly, while an icy paved runway could increase it significantly, as compared to "standard" conditions. A gravel runway might perform very similarly to a hard surface, depending on the condition.

In other words, while it's clear from the round numbers (5000' is exactly the base altitude for the column you'll use from the table, while the 101 °F temperature is exactly one unit of the 60 °F difference used for the second footnote) that this is just an academic exercise, in the real world you may have other factors to take into account, including the pilot's skill in maintaining the required approach speed of 60 mph (an even slightly faster approach can greatly increase the ground roll) and in using the brakes at their maximum effectiveness, and of course the condition of the airplane itself, especially the tires and brakes, along with the various environmental factors mentioned in the table and those I mentioned above.

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    $\begingroup$ Wouldn't a wet grassy surface be more slippery? I would assume a longer ground run in that case. Anyway, nice answer! $\endgroup$ – Peter Kämpf May 14 at 4:08
  • $\begingroup$ @PeterKämpf: "Wouldn't a wet grassy surface be more slippery?" -- the answer is a simple "it depends". You're right...slippery grass can make landing rollout longer, even as takeoff runs are also increased. See e.g. aviation.stackexchange.com/questions/49295/…. On the other hand, wet grass is often longer and the ground underneath softer, which creates more drag and will decrease the landing rollout. But you can't count on it...you won't know until you've been on the runway. Hence my use of the word "could", rather than "will". $\endgroup$ – Peter Duniho May 14 at 6:40

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