Exhaust gas speed

[Kempus]

hi guys,

Was out over St Louis the other day in the 777, looking out of doors 4 admiring the gorgeous sunset against our contrail when a collegue made an interesting statement,

"its weird to see the contrails so close but shows you how fast we're going."

Now that got me thinking, is the speed of the exhaust gasses a true reflection of our cruising speed?

Now one of newtons law's states that for each action there's an equal and opposite reaction which suggests that yes, the exhaust gasses travel at the same speed it is pushing us along at.

However i then thought thrust has to overcome drag which can vary due to aircraft attitude so more thrust would be required to maintain a certain speed and so exhaust gas speed would faster.

I'm now confused!

Any ideas?

kempus :confused:

[Mad (Flt) Scientist]

No, it's not as simple as that.

Yes, Newton's third law does state pretty much what you paraphrased. But what matters is the total mass flow through the engines times the exhaust velocity; that determines (pretty much) the gross thrust exerted by each engine. From that you have to subtract the so-called "ram drag" - the amount of air going into the engine, times that velocity. The difference between the two is the "net thrust" and THAT is what is used to overcome the drag of the airframe etc.

What that means is that an engine with a small massflow but a high exhaust velocity generates the same thrust as one with a high massflow but low velocity. Compare, say, an afterburning fighter engine with a high bypass ratio turbo fan, or even a turboprop.

Therefore, depending on various other factors there is no single relationship between exhaust velocity and aircraft speed.

[northwing]

I am 36 years out of college now so this is a bit rusty but as I remember it there is a thing called Froude efficiency which is at its maximum when the exhaust gas velocity is twice that of the aircraft. The aircraft designer will try to achieve this in the cruise.

[Mark 1]

Most civil turbo-fan engines have nozzles that expand the gas to less than the local speed of sound.

Typically at cruise it would be about 250-300 m/s for the fan nozzle and 300-400 m/s for the hot nozzle ; speed of sound goes up with sqrt(temperature) so the hot exhaust gases can expand to a higher velocity.

Trends are to lower velocities compensated with bigger areas, mostly for noise reduction purposes.

[enicalyth]

The exit velocity "v" of gas from a nozzle, or engine core, or fan is determined by adiabatic effficiency (I'll call it "effy"); the specific heat ratio k (usually called gamma), Gas Constant R, stage temperature T and the pressure ratio across the stage Pr.

Thus u = sqrt[2*"effy"*(k/k-1)RT[1-(Pr)^(k-1)/k].

A nice treatise is found in Mechanics and Thermodynamics of Propulsion by Hill & Peterson ISBN 0201 146592 pp184-185 mainly but they do go through the maths for all stages.

Also http://www.anirudh.net/seminar/ge90.pdf is handy for B777 people.

The mixing of fan and core streams mucks these undergrad figures about a bit by 1 or 2%

[MkVIII]

I would hazard a WAG that the reason your contrail was visible closer to the pipe was because it was FUGGEN COLD outside! :p

Distance a contrail is visible away from the engine is dependant upon not only EGT, but OAT and other atmospheric variables.