When performing a takeoff over a 50' obstacle, how much clearance is provided between the obstacle and the aircraft and where can that be found?
$\begingroup$ Which class of aircraft are you inquiring about? The answer may be different between airliners and sports aircraft. $\endgroup$– Cpt ReynoldsJan 18, 2019 at 19:45
Calculated figures for take-off distance required (TODR) are to only just clear a 50-foot obstacle at that distance (with gear down), and figures provided by aerodromes for take-off distance available (TODA) are the measured distance to the obstacle, with no extra clearance added.
If there's any uncertainty when they measure TODA, they'll give the most pessimistic value. The obstacle may be further away than the given TODA but no closer. Measuring distances is easy with modern equipment so it's likely to be an exact figure. However, it's rare for the first obstacle to be exactly 50 feet high. If the obstacle is (say) only 30 feet high, you get 20 feet of separation for free.
Be sure to apply the standard safety factor (e.g. 1.33) when comparing your calculated TODR with the published TODA, to ensure you get plenty of separation over the obstacle. As StephenS points out, if there are any significant obstacles in your take-off path, it's good practice to go for a best-angle climb until you overfly them.
1$\begingroup$ Please don't confuse the purpose of TODA. It is used for multi engine airplanes only that use unbalanced field lengths. By definition it is not a value to the nearest obstacle. See AIM 4-3-6. $\endgroup$– wbeard52Jan 19, 2019 at 3:48
The answer is provided in FAR Part 23. There is no conservatism involved. The distance provided is what the airplane can do.
§23.2115 Takeoff performance.
(b) For single engine airplanes and levels 1, 2, and 3 low-speed multiengine airplanes, takeoff performance includes the determination of ground roll and initial climb distance to 50 feet (15 meters) above the takeoff surface.
There is no specific clearance height since the takeoff distance, runway length, etc. will vary widely. The point of calling out that scenario in training is to get pilots used to thinking about obstacles at all and, when obstacles do exist, make it a habit to climb out at best angle until clear of said obstacles (even though that may be just a few seconds if only 50ft) rather than automatically climbing at best rate as they're used to.