# How does maximum speed vary with altitude?

Question: How does a commercial jetliner's highest possible groundspeed vary with altitude (assuming wind=0) ?

My understanding is that drag decreases with altitude, therefore maxspeed increases with altitude.

This is also what Cpt. Simon Hardy, a B777 instructor, says:

« Aircraft [referring to airliners] go faster at altitude than at low level. At sea level the aircraft [referring to a B777] can only do 330 kn. And at altitude, 30.000 ft, it can do Mach 0.86. So it's a sort of sliding scale – as you descend, you get slower. » (source)

But today I read exactly the opposite on an aviation blog, which I found curious:

« When a plane gets so high, you have to fly slower, since the speed of sound (and hence true airspeed for a given Mach number) decreases with altitude. » (paraphrasing, source)

« Real basic point: You’re flying higher, you’re flying slower. You want to go fast […] you just fly lower. » (source)

... so which is it ?

The perfect answer for me would ...
• include a graph (Y: altitude, X: maxspeed)
• include citable references

EDIT (in response to the comments below):
I specified maxspeed as the highest possible groundspeed (assuming wind=0), although I'd rather prefer not to make that distinction, because from my experience this complicates the issue more than necessary: Of course the altitude will affect the different types of speed more or less, but isn't it nonetheless possible to make an approximate statement like "higher=faster, lower=slower" and explain why that is?

EDIT2
For a concrete example, let's assume:

• aircraft = B777
• wind = 0 km/h (for argument's sake)
• weight = typical weight of a B777 ~45min into a 9 hour long haul flight
• aircraft has already reached cruising altitude

If at that point the pilot wanted to "get away" as fast as possible (let's say from waypoint IGARI), what altitude should be chosen?

Is the quoted blog post correct in saying that at an usually high altitude, the plane would fly slower, therefore it would have to go lower to fly faster?

• This very much depends on what kind of speed you are referring to. IAS, TAS, Mach, etc. There are a number of questions on the site which explain the differences and their interaction. – TomMcW Nov 17 '18 at 22:40
• Also, are you asking maximum possible speed (if yes, there will be a discussion on what that means and what side assumptions you wish to make) or maximum certified (i.e. permitted) speed? – Cpt Reynolds Nov 17 '18 at 23:05
• @TomMcW and Cpt Reynolds: I edited my question in light of your comments. And I don't ask about their interaction. – summerrain Nov 18 '18 at 7:44
• BTW speed of sound TAS varies with temperature, NOT altitude (air density) – Robert DiGiovanni Nov 18 '18 at 13:17
• Your edited statement: it's certainly possible to make a vague/general statement like "higher/faster, lower/slower" and explain why that is. I would say that this is NOT possible without defining a specific speed type. IAS = higher/slower, but TAS = higher/faster (everything else being equal). So, which do you want? (each individual type of speed is discussed elsewhere on this site) – Jimmy Nov 18 '18 at 19:52

This question isn't clear because "speed" means different things to different people, and this is also engine specific. Every aircraft will have a different speed vs altitude profile. In general...

Mach will go up, as you increase in altitude. This is because the lower density air lowers the speed of sound (in an absolute sense).

True airspeed will go up as you maintain a constant indicated airspeed. Conversely, maintaining a constant true airspeed will increase your indicated airspeed as you descend.

Normally, a jetliner should not be seeing true air speed at sea level. For jetliners, even if your engines are good enough to get you there, the aircraft has an indicated airspeed structural limit that keeps you from accelerating. You can keep the same speed (at structural limit) through higher altitude, which increases your TAS.

There is a chart here which should help show the relationships between altitude and speed:

A simplified chart for determining Mach number and true airspeed from airspeed-indicator readings:

• "Mach will go up, as you increase in altitude." TAS also? Your chart is helpful. But I don't know how to read the TAS vs altitude relationship. A simpler chart with only these two on X/Y would help me understand. – summerrain Nov 18 '18 at 8:00
• There is no TAS/altitude relationship. TAS is actually how fast you are going. In thinner air, it takes more TAS to get the same IAS (ram pressure on pitot tube, air pressure on wings). – Robert DiGiovanni Nov 18 '18 at 13:21
• Almost nice answer—if it wasn't for the huge error about speed of sound: speed of sound depends only on temperature, nothing else, neither density nor pressure (in the troposphere, all three decrease together, but that breaks down in tropopause where temperature, and thus speed of sound, stops decreasing and starts increasing again as you enter stratosphere). – Jan Hudec Nov 18 '18 at 18:42
• Actually this chart shows you reach Mach 1 at lower IAS at higher Pressure altitude. And relationship of Mach and TAS is linear, adjusted for temperature. A little confusing at first glance though. – Robert DiGiovanni Nov 19 '18 at 10:06
• @RobertDiGiovanni: re "TAS is actually how fast you are going": the question is about the maximum possible speed, i.e. how fast you CAN go, not "how fast you ARE going". / re: "There is no TAS/altitude relationship."--> Above, Jimmy says: "TAS = higher/faster" – summerrain Nov 22 '18 at 0:42

You'll fly the fastest through the air at the altitude at which your VNE and your MMO match. Higher than that, you MMO is limiting, and you can fly your MMO but your indicated airspeed will decrease as you climb -- and your TAS will decrease as well, since the speed of sound (of which you're now flying a constant fraction) is going down with the colder temperatures. Below that crossover altitude, your VNE (i.e. limit in indicated airspeed) is limiting, and it's immaterial what the speed of sound is -- you simply can't fly faster than the VNE, and you aren't getting as much benefit from the delta between TAS and IAS at lower altitudes.

The exact point of that crossover will depend on the specific VNE and MMO of a given aircraft; typically it's around 30,000' plus or minus a thousand or two.

That is NOT where airliners typically cruise, however, because along with that max speed is a LOT of fuel flow... they'll get more miles per gallon at higher altitudes (as explained in other threads). And also at speeds somewhat below the "barber pole" (i.e. the more limiting of VNE or MMO). But if you want the most TAS you can get in your airliner & fuel burn be darned, somewhere around 30k and flying at VNE/MMO will be it.

If you're trying desperately to out-run a MiG on your tail and you're willing to exceed VNE and MMO (since those 'might' kill you, but the bandit certainly will), the math would get more interesting since now max thrust and "how fast you're able to go without losing control" start to enter into the picture. And that's far enough outside the realm of realistic airline operations and pretty well into Test Pilot School stuff, that I don't think an internet forum is likely to give you any worthwhile answers there.

For practical purposes, 30,000' and flying at VNE = MMO is the answer.

It doesn’t make sense to ask for a simple answer when the question is imprecise in details and the subject matter is a little involved.

Having said that, for most civil airliners the maximum permitted speed for operations (i.e. certified limit) is the lower of VMO or MMO as explained below. VMO (max. allowed IAS) is constant with altitude, and max. allowed Mach number MMO is, too. Maximum speed (e.g. IAS/TAS) for any given altitude is the speed corresponding to the lower of the two limits.

Maximum possible speed (i.e. if you firewall the engines and don’t care if anything breaks) can be grossly different from the above and cannot be answered in general without defining assumptions, limits and a specific aircraft due to their differences.

It is both.

There are several effects which determine the maximum speed:

• At low level, a higher altitude means that the aircraft has to fly at a higher lift coefficient in order to carry its weight. This means it moves closer to the polar point of minimum drag, so it will create less drag at the same indicated airspeed. Maximum thrust drops with air density as the aircraft flies higher, so the speed increase is moderate. This is different for super- or turbocharged piston engines: Here, the maximum pressure inside the engines is limited and the boost ratio can be increased with altitude, so the available power can be maintained up to the rated altitude, so the increase in speed is more dramatic.
• At low level, airspeed is mostly limited by the maximum dynamic pressure for which the aircraft is designed and gust load limits. Exceeding this limit might cause stability problems like divergence or reduced control authority, and flying too fast into a vertical gust could exceed the maximum load factor.
• Another limit is flutter: Here, a maximum true airspeed limits how fast the aircraft can be flown. Certification limits must be 20% less than flutter onset speed.

At high altitude, the drag range with altitude is reversed: Now the airplane must fly at a higher lift coefficient that that of best L/D even at maximum speed, and now an increase in altitude will also increase drag at the same dynamic pressure. Now this effect runs in the same direction as the thrust loss from lower density, so the maximum possible speed drops quickly with altitude. But again, other limits might apply:

• Above the maximum operating Mach number M$$_\text{MO}$$ buffeting will make the flight uncomfortable.
• Exceeding the maximum Mach number for stability characteristics M$$_\text{FC}$$ reduces pitch stability below acceptable levels.
• Flying above the maximum dive Mach number M$$_\text{D}$$ might cause excessive Mach tuck which cannot be trimmed.

Boeing 777 flight envelope (picture source)

The resistance of the air to the forward motion of an aircraft decreases with altitude as the air pressure and density decreases, but the power output of an air breathing power system also tends to decrease as the amount of oxygen present in a given volume of air reduces. One objective of variable air inlet design in high performance aircraft is to increase the pressure of the air entering the engine, while reducing it's velocity. The stalling speed of an aircraft also increases with altitude, so that for example the stalling speed of the Lockheed U2 at it's maximum operating altitude (about 75,000 ft) was only 2-3 knots less than it's maximum speed at that altitude. Eventually a point is reached at which the aircraft no longer has the power available to accelerate in level flight.

Yes the blog is correct saying that "an usually high altitude, the plane would fly slower, therefore it would have to go lower to fly faster". As J. Southworth mentioned air gets thinner as you go up, commercial aircraft engines need to pump air into engines to generate thrust. This area where you can fly at max altitude with engine producing max rate is called coffin corner.

At higher altitudes, the air density is lower than at sea level. Because of the progressive reduction in air density, as the aircraft’s altitude increases its true airspeed is progressively greater than its indicated airspeed. For example, the indicated airspeed at which an aircraft stalls can be considered constant, but the true airspeed at which it stalls increases with altitude. Then there are drag constraints, wing designs as we go faster, B777 has turbofans that creates excessive drag because of those wide open intakes. Wing design is supercritical airfoil. These to limit it to 0.8-0.9 mach. beyond this you would be pushing the structural limits of aircraft.

OK, your fastest get away in a B777 disregarding fuel consumption would be based on three things: 1. Never exceed Indicated Air Speed 2. Speed of sound at the Warmest altitude available. 3. Stall IAS. Get away speed would be measured in True Air Speed.

If you were already at cruise altitude and PREPARED for this, the options would be as follows:

First rule out all (lower altitudes) where IAS Ne is LESS than your Mach limit. Think wading through water is harder than wading through air.

Next rule out all (higher altitudes) where stall IAS is MORE than your Mach limit.

Now find the warmest part of your altitude "sandwich". This is where Mach limit TAS is highest. Then calculate IAS to get Mach limit TAS for that altitude AND temperature and make your escape!

• Please see Boeing 777 chart above or Airspeed/Mach number chart below. If you do not know how to read them (it might take some time to figure them out), it may be very helpful to sit down with an instructor and learn. They answer the question quite well. BTW, humidity also has a minor role in determining the speed of sound, as well as temperatue! – Robert DiGiovanni Dec 11 '18 at 18:12