Point of no return

The point of no return (PNR) is not just an expression, it has a very real meaning in aviation. The point of no return is the point at which the aircrafts endurance is enough to either go on to our destination or turn back. If we choose to go on, we no longer have sufficient fuel to return to our destination, we have reached the point of no return. On over water legs this is an important point, if there is any emergency, our choice is already made, however suitable it may be to cater to our situation, if the weather at our destination is less than ideal, a decision should be made here whether to attempt an approach or abort and go home.

Let's say we are going from point A to point C, via point B. Point B is exactly in the middle between points A and C and there is no wind. We have only enough fuel to go from A to C and no more. Where would the PNR be? It would be at point B. Point B is halfway, and at point B we would have used exactly half our fuel. Up until we reach point B we can still change our minds and go home. At point B we can go home or we can continue on to our destination. Once we've passed point B we are committed to going on to point C.

Now let's say we have more than enough fuel to go from point A to point C, but not enough to go from point A to point C and back again. This is more usually the case with commercial aircraft. The PNR is somewhere between point B and point C, but where? Confusing the situation is the wind which is a tailwind from A to C, but would be a headwind were we to turn back to A again.

And so we find ourselves at B, needing to know how much further we could fly before we reach the PNR. We have a certain amount of fuel left;

Fuel on board 14000 Kg.

And we can calculate how much fuel will be required to fly back from where we are (B) to home (A.)

Fuel required to fly back to A from B 4000 Kg

We do this and subtract it from the fuel we have on board, whatever is left over is the amount of fuel we have available to fly out to the PNR and back to B.

14000 - 4000 = 10000 Kg

If the wind was nil, we could divide by the SGR to find how many miles we could fly using this fuel, halve the distance and we would have our answer. Or to put it another way, divide by twice the SGR, the SGR out being the same as the SGR back. This is the heart of the problem - wind and different aircraft configurations mean that the SGR out is almost never the same as the SGR back. But the equation is still the same;

Fuel at B after fuel back to A is subtracted;

10000Kg

Divided by SGRout + SGRhome;

10000 / (8.5 + 10.7) = 520nm

EDIT - It's been pointed out that I didn't explain what SGR means. The SGR is the specific ground ratio, or the amount of fuel used per distance of ground covered, and varies by fuel flow, airspeed and head/tail wind. In this case the SGR is KG of fuel used per ground NM covered. The B727 conveniently averages 10 KG per NM on average in cruise configuration. A headwind increases the SGR, increasing the amount of fuel used per NM, while a tailwind decreases it.