Kaddyuk From Wallis and Futuna, joined Nov 2001, 4126 posts, RR: 25 Posted (8 years 5 months 3 weeks 3 days 12 hours ago) and read 32767 times:

Hey Guys (& Girls)

I'm putting together a spreadsheet of TSFC's for different engine types. I'm also trying to put together a crude range calculator for engines on different aircraft.

I've just started to see if it can even be done and i'm not getting the ranges i would expect. My workings are as follows, does anyone see where i'm going wrong?

CFM56-7B20 is rated at 91.6kN of Thrust. At 100% N1, it burns 0.91KG of Fuel per second. This gives it a TSFC of 0.035752

TSFC = FF per Hour (KG/HR) / Force Of Engine Produced (N)

Fuel Flow Per Hour @ Cruise = TSFC * Force Of Engine @ Cruise

FFPH @ Cruise = 0.035752 * 77.8kN (Force @ Cruise = 80% of Max Force Avail)

This now means that the FFPH at cruise is around 2784.6kg per hour which when you multiply by two (for 2 engines) is equal to 5569.2.

Eurocontrol produce figures of average fuel burns of aircraft flying through their airspace. For the B737-700 series, i can expect to burn 43 kg per engine per minute at cruise, 450kts, FL330.

Which when calculated is 43 * 60 (FF Per Hour) multiplied by 2 (for 2 engines) and that comes to 5160. This means my numbers are not that far from the Eurocontrol data (and could be closer just by reducing the cruise N1)

Now to calculate range at cruise divide total fuel available (Max Fuel Capacity) by the FF Per Hour to get the Time that you can fly... Which when multipled by your speed will give you range.

My problem lies here, I've got data which says the B737-700 series engine has a fuel capacity of 21000kgs which at 5569kgs per hour gives the aircraft a mission time of 3hrs 46mins and at 450kts a total range of 1711nm (Which is WAAAAY off the actual range of 3100nm).

Technically, i should be calculating ranges further than what the manufacturer say because i'm assuming the aircraft to be in flight with full tanks.

Anyone help me out?

Whoever said "laughter is the best medicine" never had Gonorrhea

Jetlagged From United Kingdom, joined Jan 2005, 2577 posts, RR: 25
Reply 1, posted (8 years 5 months 3 weeks 3 days 9 hours ago) and read 32767 times:

The main problem lies in the fact that you don't know what cruise thrust is and assume it is 80% of take off thrust. In fact it will change throughout the flight and will depend on the takeoff weight too.

Also tsfc is not constant and varies with power setting, flight condition, etc.

That's not to say approximations aren't possible, but it would be better to take several conditions for which you know the range, then using your tsfc figures, work out a cruise thrust factor which gives you the same answer. Note how this cruise thrust factor varies. If it's fairly constant use that figure for other estimate, or take an average.

That would give you a better estimation for other types, but it can only be a rough estimate at best.

The glass isn't half empty, or half full, it's twice as big as it needs to be.

Vikkyvik From United States of America, joined Jul 2003, 10344 posts, RR: 26
Reply 3, posted (8 years 5 months 3 weeks 3 days 9 hours ago) and read 32767 times:

Quoting Kaddyuk (Thread starter): FFPH @ Cruise = 0.035752 * 77.8kN (Force @ Cruise = 80% of Max Force Avail)

I'm not quite sure how this applies to the actual FFPH, but it should be noted that the engines will not be producing 77.8 kN at cruise altitude. You're using 80% of the engines' SLST, which would only be applicable were the engine at sea level.

The thrust available reduces as the altitude increases. I can't remember actual numbers, but engines at cruise altitude are actually producing under 50% of their rated thrust, if I remember correctly.

~Vik

EDIT: Meant to say that thrust at altitude is approximately your thrust at sea level multiplied by the ratio between density at altitude and sea level density. This means that at 30,000 feet, jet engines would be able to produce ~37% of their rated thrust (this is just an approximation).

Kaddyuk From Wallis and Futuna, joined Nov 2001, 4126 posts, RR: 25
Reply 4, posted (8 years 5 months 3 weeks 3 days 8 hours ago) and read 32767 times:

Quoting Jetlagged (Reply 1): Also tsfc is not constant and varies with power setting, flight condition, etc.

TSFC is a constant, its a ratio between fuel flow per hour and the amount of force produced from that fuel.

Quoting Vikkyvik (Reply 3): The thrust available reduces as the altitude increases. I can't remember actual numbers, but engines at cruise altitude are actually producing under 50% of their rated thrust, if I remember correctly.

~Vik

EDIT: Meant to say that thrust at altitude is approximately your thrust at sea level multiplied by the ratio between density at altitude and sea level density. This means that at 30,000 feet, jet engines would be able to produce ~37% of their rated thrust (this is just an approximation).

Now that is one idea that i was thinking about... Thanks! I'll whack that into my equations and see what i can get...

Whoever said "laughter is the best medicine" never had Gonorrhea

Jetlagged From United Kingdom, joined Jan 2005, 2577 posts, RR: 25
Reply 5, posted (8 years 5 months 3 weeks 3 days 8 hours ago) and read 32767 times:

Quoting Vikkyvik (Reply 3): The thrust available reduces as the altitude increases. I can't remember actual numbers, but engines at cruise altitude are actually producing under 50% of their rated thrust, if I remember correctly.

Well under 50%, thrust reduces with the ratio of static air pressure. At 35,000 feet this will be about 24% of sea level thrust. Also the assumed 80% for cruise is a bit high I'd guess.

If Kaddyuk derives his thrust factor empirically as I suggested in the first reply he could get a reasonably close answer.

The glass isn't half empty, or half full, it's twice as big as it needs to be.

Vikkyvik From United States of America, joined Jul 2003, 10344 posts, RR: 26
Reply 6, posted (8 years 5 months 3 weeks 3 days 8 hours ago) and read 32767 times:

Quoting Jetlagged (Reply 5): Well under 50%, thrust reduces with the ratio of static air pressure. At 35,000 feet this will be about 24% of sea level thrust. Also the assumed 80% for cruise is a bit high I'd guess.

If Kaddyuk derives his thrust factor empirically as I suggested in the first reply he could get a reasonably close answer.

All I was saying is that if the engines are producing 80% thrust at cruise, they're actually producing 80% of your thrust available, which, at cruise, will be somewhere in the range of 20-40%. so (0.8)(0.3) = 24% (not the same 24% that you mentioned). I'm a bit foggy on this stuff, but I was taught that jet engine thrust is proportional to density ratio as opposed to pressure ratio. I might be wrong on that though. Either way, there's no way those engines are producing 70+ kN at altitude.

Kaddyuk From Wallis and Futuna, joined Nov 2001, 4126 posts, RR: 25
Reply 7, posted (8 years 5 months 3 weeks 3 days 7 hours ago) and read 32767 times:

Bingo... I get sensible numbers now coming out of my equation... My range is higher than the actual but only by about 100nm... Which i guess i can put down to the fact that i'm assuming the cruise distance from full tanks (Which the aircraft will never have full tanks to start a cruise)

Whoever said "laughter is the best medicine" never had Gonorrhea

Jetlagged From United Kingdom, joined Jan 2005, 2577 posts, RR: 25
Reply 8, posted (8 years 5 months 3 weeks 3 days 7 hours ago) and read 32767 times:

Quoting Vikkyvik (Reply 6): I think we are saying the same thing. Maybe?

Exactly, I was only trying to show it that 50% was conservative, and of course as you say it is 50% of the 80% or whatever.

I'm not sure if it's density or pressure. But there's not a huge difference when we are dealing with such approximations. Engine thrust data is usually normalised with ambient pressure ratio, but of course that doesn't mean it varies exactly like that, so you could well be right on the density relationship.

The glass isn't half empty, or half full, it's twice as big as it needs to be.

Liedetectors From United States of America, joined Jul 2005, 360 posts, RR: 0
Reply 9, posted (8 years 5 months 3 weeks 2 days 19 hours ago) and read 32767 times:

This would be a no brainer if someone here who works for GE can go run the engine deck/engine cycle model for a range of cruise power settings or match to a hand full of thrusts.

WILCO737 From Greenland, joined Jun 2004, 9118 posts, RR: 76
Reply 10, posted (8 years 5 months 3 weeks 2 days 15 hours ago) and read 32767 times:

AIRLINERS.NET CREW HEAD MODERATOR

Hey,

it looks pretty close to the real, but at some point I guess you mixed up pounds and Kilogramms!

I flew 737-700s and we calculate with an average fuel flow during cruise of 2400 KGS/hour for BOTH engines, so 1200 KGS per hour per engine...

Sometimes it is a bit higher, when you fly faster or lower!

Quoting Kaddyuk (Thread starter): This now means that the FFPH at cruise is around 2784.6kg per hour which when you multiply by two (for 2 engines) is equal to 5569.2.

So, if you take pounds here, then you are close enough!

F14D4ever From United States of America, joined May 2005, 319 posts, RR: 4
Reply 11, posted (8 years 5 months 3 weeks 1 day 3 hours ago) and read 32767 times:

You really ought to be using the Breguet range formula, which is:
Range = V*(L/D)* ln (Winitial / Wfinal) / (g*SFC)
This formula properly accounts for the change in aircraft weight due to fuel burn, and should get you closer to realistic numbers.

At FL330/Std. Day the CFM56-7B20 burns closer to .517 Kg/sec at about 26 kN thrust.

Timz From United States of America, joined Sep 1999, 6902 posts, RR: 7
Reply 12, posted (8 years 5 months 3 weeks 1 day 3 hours ago) and read 32767 times:

Quoting Kaddyuk (Reply 4): TSFC is a constant, its a ratio between fuel flow per hour and the amount of force produced from that fuel.

Where'd you hear that? Jane's used to give SFCs for engines; at 35000 ft, cruise thrust the SFC they gave was maybe 70% more than at sea level, maximum thrust.

F14D4ever From United States of America, joined May 2005, 319 posts, RR: 4
Reply 13, posted (8 years 5 months 3 weeks 18 hours ago) and read 32767 times:

Quoting Kaddyuk (Thread starter): CFM56-7B20 is rated at 91.6kN of Thrust. At 100% N1, it burns 0.91KG of Fuel per second. This gives it a TSFC of 0.035752

That TSFC is only valid at that thrust rating, and only at the flight condition at which the rating occurs.

As Jetlagged and Timc have stated, TSFC is not constant; it varies with altitude, flight Mach number, ambient temperature, and throttle setting. To calculate aircraft range at FL330/cruise, you must use the TSFC calculated for that flight condition and throttle setting. I gave you the numbers you need: .517 Kg/sec @ 26 KN thrust. Now you need to go find the Lift/Drag ratio for the aircraft in cruise configuration, and aircraft weights at begin and end of cruise.
Plug those nums into the Breguet formula to obtain a meaningful range answer.