PoH says airplane climbs steeper at higher weight. Why? How?

Question

Here's a puzzle. Looking at the PoH of my aircraft, it appears that the climb angle (distance to clear a 50 foot obstacle, starting from the end of the ground roll) is shallower at lower weight than at max gross.

That doesn't make sense to me - oughtn't the climb slope to be steeper at lower weight?

For example, the PoH claims that at sea level, 20 C and 1430 lb, the ground roll is 424 feet, and it needs 972 feet (total, including the ground roll) to clear a 50' obstacle.

At 1320 lb (also 20 C and sea level), it says ground roll is 210 feet and 782 feet to clear the 50 feet.

So the climb slope at 1430 lb is (972-424)/50, or 10.96:1.

And the climb slope at 1320 lb is (782-210)/50, or 11.44:1. Shallower, at lower weight.

I get similar results at all temperatures and pressure altitudes.

What's going on?

Answer 1

There are three stages to a short field takeoff over an obstacle- the ground roll, where the airplane accelerates to the minimum airspeed necessary to leave the ground, a period of further acceleration to Vx, and then a climb at Vx. I believe your analysis is flawed because it ignores this acceleration period.

The ground roll is the distance from the beginning of the takeoff run to the moment the airspeed is sufficient to become unstuck. When the aircraft is lighter, the required airspeed to become unstuck is less. So the heavier aircraft will be going faster at the end of the ground roll than the lighter aircraft will be.

The climb angle of the lighter aircraft is certainly steeper once both have reached Vx. But the lighter aircraft is further from Vx at the moment the ground roll ends and spends a little more distance accelerating to reach the same airspeed.

Answer 2

This is a very interesting question involving an amphibious aircraft, the Super Petrel LS.

Building on the answer by Chris, we see that take-off from water would involve "muddy/soft" field technique.

Indeed, the lighter plane would lift out of the water at a slower speed, therefore requiring more time to accelerate.

On dry land, it would be smarter to hold off on rotation until reaching Vx in any case, as rolling at low AoA is less draggy than flying. Only when field conditions create greater drag is it advantageous to haul it into the air at a lower airspeed.

This is why many planes take off "clean", no flaps, using a greater ground roll and climb out at Vy. Even at Vx with flaps, keeping drag as low as possible by delaying rotation can be the most efficient way to gain airspeed.