Is it permissible/advisable to take off with a tail wind if there is a significant down slope? On the other hand, what about landing with a tail wind if there is a decent up slope. The charts I am looking at suggest the TODR and LDR are less with a tail wind provided the slope is significant. 2 degrees of slope cancels out about 10 knots of tail wind. Can anyone assist?

GA aircraft usually have a limit imposed for downwind take-off of landing so that limit will apply in any case. Having said that it certainly would be better to take off with a slight downwind component when a down slope is 2% or more.

Propeller-driven aeroplanes are notoriously bad at climbing hills because the power is not being delivered directly to the wheels. That's one reason why aeroplanes find it heavy going when taxiing over a soft surface. Likewise, up-hill take-offs should be treated with great caution. This is compounded by the likelihood that the terrain beyond the up-wind threshold may often continue to slope up from the runway.

Most helpful. Thank-you

Some additional points -

(a) significant slope will give you a one-way strip operation - see many examples from PNG

(b) probably not going to be a problem for lighties but, for some larger aircraft with big engines, a standing start, high power takeoff in tailwind conditions can sit the aircraft on its tail .. occasionally this limits the maximum tailwind.

(c) concur with Bob .. avoid uphill takeoffs like the plague if the alternative is acceptable ...