Help with a calculation

[PTK]

I'd like to perform a calculation of what it costs to be carrying extra fuel on a flight above and beyond of what's needed for the flight.

In terms of fuel consumption and speed penalty due to the extra weight of the unnecessary fuel.

Any ideas where to begin?

Strictly out of curiosity!

[Hank]

Start with your performance charts. Find speed at your desired altitude and power. Interpolate between the weights shown.

if your luck runs like mine, you'll have to interpolate for altitude, do it again for power setting and a third time for weight.

[ArtVandelay]

A rough calculation, for a 4 hr flight, you'll burn an extra 1.5 gal for an extra 340lbs, so extra fuel will be less, so less than a gallon of fuel, that doesn't include the climb fuel consumption.

This is using the tables in the old J POH, I don't like the newer POH with graphs instead of tables.

[carusoam]

Where the extra weight shows up in performance...

1) Slower Acceleration zero to cruise speed.  More time at FT climbing through lower altitudes.

2) T/O distance.  More FF at full rich for a longer period of time.

3) Slower Climb rate. More time spent at FT and 2-300°F ROP.

4) How the AOA drag is effected by the excess fuel weight.  The big drag change shows up as slower IAS

5) How the trim setting is effected by WnB of the excess fuel weight.  How much does your WnB get effected by excess fuel?

6) excess power related to AOA used during slow flight around the TP.

7) Excess brake wear related to stopping distance caused by excess fuel weight.

Peter, you would have to be really good at taking measurements to define these.  It would probably include at least a three way course at different weights.

As usual, I am still a simple PP. not a CFI, mechanic or aeronautical engineer. 

Best regards,

-a-

[Piloto]

Don't forget the headwinds and tailwinds. They will be a bigger factor than the actual weight. A tailwind can save an hour of fuel on a long trip while a headwind can add an hour.

José 

[Hank]

That's true, Jose. My worst headwind added just over two hours to a two and a half hour flight--2:20 out, 4:45 back, straight-and-level groundspeeds as low as 68 knots.

But Peter asked for calculations. Now that he's been playing with Perf Tables, paper, pencil and calculator, we tell him that the effect is nearly negligible, unless he reads Anthony's post and goes easy on the brakes and rolls out longer when heavy. But realisticly, the max landing fuel in my plane shouldn't vary more than 40 gals, or 240 lbs. A J, with 64 gal tanks, may vary 50-55 gals. or up to 330 lbs. Both compare to landing with minimum reserve fuel, so usually much less. 

I learned something here. Full fuel is like adding my CFI on top of minimum fuel! Still leaves almost half of my useful load available. The control feel is definitely lighter, and landing is can be a more ethereal experience when light. 

[Bob - S50]

There are lots of variables that you have to consider before you can figure it out.

What is the minimum fuel you are willing to land with? 30 minutes?  45 minutes?  1 hour? 10 gallons?

How long is the flight?  1 hour? 2? 3?

These two values will determine the maximum weight difference you can control.

What altitude do you plan to cruise at?  You can waste more gas cruising at the wrong altitude (even no wind) than you can save by getting there with minimum fuel.

With all that said, I looked in my '78 POH.  It gives performance for two weights, 2740 and 2300.  That's a 440 lb difference which is more than a full tank of gas (372 lbs) so the max difference you can have based on fuel load is less than the book values.  Assuming you want to land with an hour of fuel, that makes the max difference 55 gal or 320 lbs.  However, assuming you want to fly for an hour the max difference with warm up and climb to a low altitude would be about 45 gallons or 262 lbs.  For a 2 hour flight it would be 209 lbs or less than half the two values in the book.

Look at the range values.  They include warm up, takeoff, climb at Vy and cruise with a 45 minute reserve.  If you start with those numbers, you can't have excess fuel because you are burning all of it that isn't reserve.

At 8000', 2400 RPM, WOT, 9.1 GPH; the difference in range is only 24 NM.  At the gross weight performance it would only take 1.39 gallons to fly the extra distance.  So if you only flew half that distance you could only save 27.3 gallons (3 hours at 9.1 GPH) of fuel load or 159 lbs at start.  That's just over 1/3 the book value differences for 1/2 the time or about 1/6 of the fuel burn.  So I would guess you could save maybe 1.39 x 1/6 = a quart of gas on a 3 hour flight at 8000'.  Something under a dollar for increased pucker factor.

At 2000', the difference in range is only 11 miles, or less than half the difference found at 8000' so maybe a pint on a 3 hour flight.

We can waste more gas than that with technique.  Idling at full rich on the ground. Slow cleaning up after takeoff.  Climb speed.  Failing to lean during the climb. Cowl flap management in the climb. Cruise altitude chosen based on distance to fly.  Cruise altitude chosen based on winds. Cruise mixture. Excess maneuvering to enter the pattern and land.  Putting the gear down early.  Going full rich (if you do) early.

Interesting academic question though.

And that's not to say I never plan to get there with minimal extra fuel.  I'll sometimes plan to get to a planned fuel stop with 10 - 15 gallons of fuel if the price of gas is significantly cheaper there.  For example, I flew an Angel Flight from S50 (Auburn, WA) - PWT (Bremerton, WA) to pick up my passenger.  Flew to ONO (Ontario, OR), then back to LGD (La Grande, OR) which was on my way home, to buy gas.  Fuel was cheaper at home than at PWT or ONO.  I put on just enough at home to get to LGD with 10 - 15 gallons.  Fuel at home was about $5/gallon but with the Phillips 66 rebate, it was only $3.50 at LGD.  I then put on enough at LGD to park at home with our partnership agreed 30 - 35 gallons.  So I bought as much fuel as possible at the lowest price available.  Saved about $60.

[jrwilson]

There's an app for that.  Aircraft ferry fuel calculator, its free.  I think it mostly calculates cost, rather than speed penalties.

[1964-M20E]

I'm sure you can set up a spread sheet to do this however, at the end of the day you spend more time computing, less time flying not really saving a whole lot of time. JMHO

As for planning your fuel stops to save money $/gallon the benefits of that are also questionable and it costs you more time and the same can be said for tanking fuel. 

So at the end of the day I make sure I have plenty of fuel on board to cover the trip and will not leave with less than 30 gallons on board unless fuel is not available at the airport where I am.  There have been a few occasions where I have stretched the envelope but still landed with 10 gallons of gas or more and that is a good solid hour in my plane.

 

[Jerry 5TJ]

Based on many cross-country legs I know my "C" picks up about a knot for every 50 to 70 pounds reduced load.  That's what I see on a long flight as fuel burns off weight.  Two hours after leveling off the plane is about 2 Knots true faster at 2400/22" power.   

As I am the sort of pilot who feels he never has too much fuel aboard (unless the airplane is on fire) I generally carry extra fuel and go a knot or two slower.

[steingar]

Lot of things I'd leave behind to get a bit faster.  Gas just ain't one of them.