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Thrust required during turn versus climb

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Thrust required during turn versus climb

Old 5th Mar 2018, 08:17
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Thrust required during turn versus climb

Hi all,

Got a question,

Forgot the relevant formulaís a long time ago, but what requires more thrust? A level turn at 1.3g or a climb with 100fpm. Talking about B737 7 through 9 series

Reason Iím asking is we are getting a FMS software update that now displays a T or B behind the max altitude to indicate wether you are thrust limited or buffet limited at the max altitude.

Recently had a discussion with a check airman during a check when flying close to the max altitude. I briefed my college that when any turn where given by ATC we would select bank angle 10 first before executing the turn because we were flying close to the max altitude and were thrust limited to maintain airspeed during a turn.

The check airman pulled out a chart indicating max altitude and where it had a asterix behind an altitude to indicate when you were thrust limited. However the chart indicated thrust limited based on a 100fpm climb.

This says nothing imho about the ability to maintain airspeed in a bank!

Of course I would not execute a turn at 39 degrees at altitude(1.3g) but what would require more thrust, A bank angle of say 25 degrees at altitude or a 100fpm climb?

Iím afraid that the new software update is gonna lead to a false sense of security when executing a turn at max altitude.

Airplane concerned is B737(7,8,9). I have never flown the B737 where the upper and lower amber bands touch each other, in other words you can always turn theoretically with 39 degrees of bank before hitting high or low speed buffet, however when flying close to max altitude you donít have the ability to maintain speed at that bank angle.

So, what requires more thrust? A climb with 100fpm residual climb or a bank angle of 39 degrees and what is indicated by the T behind max altitude in the FMS: the ability to maintain airspeed or the ability to sustain a 100fpm climb.

Iíve forwarded the question to our flight technical department but am curious as to opinions here?

Relevant documentation FCOM performance inflight long range cruise max operating altitude tables and FCTM max altitude.
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Old 5th Mar 2018, 16:22
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So, what requires more thrust? A climb with 100fpm residual climb or a bank angle of 39 degrees and what is indicated by the T behind max altitude in the FMS: the ability to maintain airspeed or the ability to sustain a 100fpm climb.
I cannot answer that. However:

Rate of climb = excess power divided by weight
Excess power = excess thrust x velocity
Assume additional drag (and therefore thrust) for turn varies as square of the coefficient of lift
Assume flight at min drag speed to simplify

39 degrees AoB is a load factor of 1.28. Therefore the lift coefficient increase is 1.28 x whatever it was. 1.28 squared is 1.64. In other words, the induced drag [as opposed to total drag] is 64% greater than straight and level.

Total drag is lift dependant plus zero lift drag. At min drag speed straight and level that is simply 2 times the lift dependant drag, whilst at 39 deg AoB the total drag is now 2.64 times the lift dependant drag. In other words, drag and therefore thrust is 32% higher than straight and level. That deals with the turn thrust.

For climb, if you know your speed you can easily work out your excess thrust at 100 fpm:

ROC = (Excess thrust x velocity)/weight. Rearranging:

Excess thrust = (ROC x weight)/velocity

Now given flight at Vmd of say 100kts and ROC of 100 fpm (which is 1 knot):

Excess thrust = (1 x weight)/100
Excess thrust = weight/100

...eg @ 10000lb weight you would need 100lbs excess thrust to acheive 100 fpm.

...I'll just put that one out there for review. However, I suspect that if you factor in all variables in detail for high speed and high altitude flight you will get a more relevant answer than my crude theory would lead you to.

Last edited by oggers; 5th Mar 2018 at 16:42.
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Old 5th Mar 2018, 17:19
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Another Take on this Question

Let me take a different approach to the questions asked.

Let's assume that the L/D involved is 20 and that the airplane is flying at Mach 0.8 at 30K feet such that its true airspeed is about 800 ft/sec.

Now the question of the thrust increase needed for a level turn:
Lift must increase by 1/cos(phi). Assuming L/D remains about the same below are the percentage increases in thrust required as a function of bank angle (thrust increase proportional to lift increase):
Bank Angle Thrust Factor (1 = trim for level flight)
----------------------------------------------------
0 (level) 1.000
10 deg 1.015
20 deg 1.064
30 deg 1.155


Now the question of thrust increase needed for 100ft/min climb:
- 100 ft/min when flying at 800 ft/sec represents a flight path angle of 0.002 radians (100ft/min) / [(800ft/sec)*(60sec/min)] that is equal to 0.12 degrees.
- This requires an increase in thrust of 0.2% of the airplane weight.
- With an L/D of 20, the level flight thrust required is 5% of weight.
- The increased thrust for the climb is 4% (0.2% / 5%) compared to the thrust required for level flight.

Comparing these results, the thrust required to be able to climb at 100 ft/min is the same as the thrust required to fly a 16 degree bank turn at the same speed. The assumption here is that you are thrust limited and not CL limited so that you are able to increase AoA enough to get the needed additional lift for the turn while maintaining the current speed.


It seems to me that limiting bank angle to 10 degrees when in a thrust limited condition is prudent.

Hope this helps.
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Old 5th Mar 2018, 20:32
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Yes, it does! Thanks!

Btw, pretty impressive both!!

Last edited by flyburg; 6th Mar 2018 at 07:26.
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