Calculating the time to Single engine Point of no return

[flyndad]

Fuel on Board- 500 lbs
All Engines TAS 150 KTS
All Engines Fuel Flow- 150lbs/hr
One engine out TAS/ 95 KTS
One engine out Fuel Flow 95lbs/Hr
Average trip winds/40 kt Headwind
Reserve 100 lbs

Can anyone explain the easiest way to compute this?

[digits_]

Think about it logically. You want to know how far you can fly (distance d) before you are unable to return back.

Fuel is basically time. Let's calculate how long it would take you to fly d nautical miles:
OutboundTime OT
OutboundSpeed OS = (All engines TAS - headwind) = 150 kt - 40 kt= 110 kt

OT = d / OS

And how long it would take you to fly back the same distance:
ReturnTime RT
ReturnSpeed RS = (one engine tas - headwind) = 95 kt + 40 kt = 135 kt

RT = d / RS

We now know how long we can fly. How much fuel can we burn? 500 lbs - 100 lbs reserve = 400 lbs. That's our TotalFuel TF
AllEngineFlow AEF = 150 lbs/hr
OneEngineFlow OEF = 95 lbs/hr
TF = AEF * OT + OEF * RT
= AEF * d / OS + OEF * d / RS
= d ( AEF / OS + OEF / RS )

If we fill in all the values we get:

400 lbs = d ( 150 lbs/hr / 110 kt + 95 lbs / hr / 135kt )
= d ( 1.8 lbs/NM)

Which means
d = 400 lbs / 1.8 lbs/NM = 222.22 NM

[flyndad]

Thank you Sir.

[photofly]

150lbs/hr to get 150 KTAS - two engines turning
95lbs/hr to get 95 KTAS - one engine turning

Implies the aircraft will go exactly the same distance (in the same direction) on one engine as on two (albeit slower) - is that realistic? That means if you're flying downwind you'll increase your range by shutting one down right after takeoff...

[digits_]

150lbs/hr to get 150 KTAS - two engines turning
95lbs/hr to get 95 KTAS - one engine turning

Implies the aircraft will go exactly the same distance (in the same direction) on one engine as on two (albeit slower) - is that realistic? That means if you're flying downwind you'll increase your range by shutting one down right after takeoff...

Isn't that fairly common in light twins?
Blue line is typically significantly more than 50% of the cruise speed. Granted, you'll also burn more on one engine at nearly full power, but if you run the numbers for some king air models and a travel air or similar, there's hardly ever a situation where you'll cover less ground on one engine.

[Aviatard]

150lbs/hr to get 150 KTAS - two engines turning
95lbs/hr to get 95 KTAS - one engine turning

Implies the aircraft will go exactly the same distance (in the same direction) on one engine as on two (albeit slower) - is that realistic? That means if you're flying downwind you'll increase your range by shutting one down right after takeoff...

Seneca I numbers because I happen to have those handy:
Two engines 75% - 165 mph - 20.6 gph
One engine 75% - 120 mph - 10.3 gph

You get 75% of two engine speed for 50% of fuel burn.

[photofly]

150lbs/hr to get 150 KTAS - two engines turning
95lbs/hr to get 95 KTAS - one engine turning

Implies the aircraft will go exactly the same distance (in the same direction) on one engine as on two (albeit slower) - is that realistic? That means if you're flying downwind you'll increase your range by shutting one down right after takeoff...

Isn't that fairly common in light twins?
Blue line is typically significantly more than 50% of the cruise speed. Granted, you'll also burn more on one engine at nearly full power, but if you run the numbers for some king air models and a travel air or similar, there's hardly ever a situation where you'll cover less ground on one engine.

That makes sense for a twin piston aircraft at low altitude. I guess I misread the question as being about something faster and higher-flying (which it obviously isn't, if the single engine speed is 95KTAS, so my bad, there). Presumably not true for a transport aircraft? The BA 747 that shut one engine down after departure from Los Angeles had to land short of Heathrow for fuel in Edinburgh (I think) because of its inability to cruise at the planned altitude, leading to reduced range. Where would the crossover in overall fuel efficiency be?

Question for someone with a light twin handbook to hand: which is more efficient - throttling back to 40% power on both engines, or shutting one down and running the other at 80%?

The "surprise" and probably incorrect conclusion is that in theory if you have concerns about your fuel situation, shutting down an engine (not a typical move) and completing the flight on just the other, would help.