Jazzy

Just out of curiosity...

It is my understanding that the s.o.s. at sea level is around 680 mph. Of course this is dependent upon atmospheric pressure, humidity, temperature, etc.

Does anyone have info regarding the s.o.s. and how much it decreases at different elevations above sea level? Say, in 100' increments and not accounting for variations of the above mentioned variables. (If temperature has great bearing on the results then please mention it also.)

I've done some calculations regarding prop tip speed using 600 mph as the s.o.s. at around 1400' above sea level. I'm wondering how close I am.

Thanks,
Jeff

Tall Paul

The speed of sound at sea level is 661.4748 knots.
It varies with temperature, which varies with altitude.
.
a=a0*(t/T0)^.5
a0 speed at sea level 1116.44 ft/sec
T0 absolute temp at sea level, deg K 288.16
The lapse rate with altitude is :
t=15-.0019812*pressure altitude.. deg C
or
t= 59-.00356616*pressure altitude.. deg F

Geistware

My Feedback: (16)

I know you have the equation, but I was understanding that the SOS was due to density since sound needs molecules to propagate. The higher the density the faster the speed. That is why sound travels faster at higher elevations and different materials.

Tall Paul

Here's a table of the atmospheric quantities that interest aerodynamicists...
The unfortunate 700 pixel limit here requires a little eyestrain...

Tall Paul

"The higher the density the faster the speed. That is why sound travels faster at higher elevations..."
Yes, to sentence 1.
No. to sentence 2. Air is LESS dense with altitude.
The speed of sound diminishes with altitude.
A colder than standard day at altitude will result in a faster speed of sound relative to a standard day at -that- altitude. A hotter than standard day results in a slower speed of sound..

drela

The speed of sound in any one ideal gas (like air) depends ONLY on the temperature. The density and/or pressure are immaterial. The higher the temperature, the faster the speed of sound. For air, the specific formula is

a = 20.04 sqrt(T)

where a is the speed of sound in m/s, and T is the air temperature in Kelvin. Paul gave the same equation, but in ratio form relative to sea level values.

A gas other than air will have the same sqrt(T) dependence on the temperature, but the "20.04" constant will be different. Typically, smaller molecular weights have a larger constant, and vice versa. So the speed of sound in helium is considerably larger than in air at the same temperature.

Flypaper 2

Iread somewhere, at 40,000ft average sos was 760mph. I can see it at higher altitude, with the thinner air, one would have to go faster to compress the thinner air enough to go through the sound barrier

Tall Paul

The speed of sound at the tropopause.. approximately 36,000 feet is 970.9 ft/sec. It's constant from there to over 100,000 ft.
As altitude increases, the plane must fly faster to stay up, because there's less air to support it.
This results in gliders like the U-2 running into Mach buffet while flying at very low indicated airspeeds, but high true airspeeds.. about .7 Mach.. a speed it could not possibly get to at sea level.

warbirdz1

Jazzy....When flying at altitudes above 20k ft the indicated airspeed starts to decrease at a good pace..to make flying easier above 20,000 ft the mach number was employed because it is much better at being user friendly...like Drela's post mentions it is only dependant on temp......modern aircraft use ADC,s( air data computers) to compute Mach Number ...at say 20,000 ft your indicated airspeed is 350 knots now check in @ 37,000 ft it might now be 240 knots indicated where by using a mach number a pilot could see .80 all the time....also keeping in mind the air thins out the higher you go making "Buffet" margins easier to define...because there are low speed margins (encroaching stall area) and high speed margins(airframe limits) and these margin areas compress as the altitude increases....temperatures in the 35,000 to 40,000 ft altitudes can be 50* to 60* below zero.....If you compute your props tip speed , I know for full scale aircraft anything over roughly 650ft/sec props start making lots of noise...like a T6 prop...really wails @ t/o power........Bill....

Jazzy

Thanks to everyone, especially Tall Paul.
I knew that the denser the medium the faster the sos. The excellent table you provided both confirms what I already knew and enlightens that which I was in err.
Just what I was looking for!

Thanks again,
Jeff

Lt. Dan

My Feedback: (21)

Here's a little Gee Whiz, when crewing DC-10's, at cruise, we usually had about a 150 knot split between IAS and TAS. As said before, the reduced IAS being attributed to the less-dense air entering the CADC's.

At about 30,000ft + we would be cruising at about 300KIAS but out TAS was about 450.

StarskiPZ

There are other parameters apart from temperature.

In laymans terms, s.o.s is greatest at sea level - or where air density is greatest.

As you gain altitude the air becomes less dense untill you actuall thin out into space, where density approaches zero ( over 400,000 ft ).

Gravity keeps dense air down - obviously.

Temperature causes air to rise because it expands the 'mass' making it 'lighter'.

I have no data on how moisture content effects s.o.s

BMatthews

Well, this is an eyeopener. I always figured it was the altitude related density. And here it's the temp. Learn something new every day......

Speaking of U-2's. One of my favourite story lines about these remarkable planes is the condition that determines the plane's max altitude.

One of the books I read described how the plane could climb until the rising stall speed related to the altitude density boxed the plane's speed up against the Mach 1 barrier. They would climb until the stall to supersonic range was somewhere around 10 knots or so and at that point the auto pilot's most crititical function was to maintain the speed. In a turn, which at that height were all of a HUGE radius, any signs of buffeting could be either the faster outside wing going supersonic or the slower inner wing reaching the stall speed. The reaction was to very slightly dive the plane as it was better to go farther into the supersonic region than risk a tip stall on the inside wing. If the buffet kept up or worsened then the plane was gently coaxed to nose up to a slightly slower speed to reduce the outer tip below the critical Mach number. Making the wrong move and stalling the inner panel could quickly result in a spin that could only be recovered when the plane had reached some decent air many thousands of feet lower. I seem to recall that such a spin would flame out the engine at the same time. All in all not a nice situation to be in.

Heady stuff indeed to us ground bound folks.

drela

That's backwards. On a hot day the speed of sound is GREATER, and vice versa.

As stated before, the speed of sound depends ONLY on the air temperature. The air density is irrelevant.

Jazzy

Mark, the table tells all.
For example: The speed of sound in water is MUCH greater than that of air due to the density of the medium.
With all due respect, you've got it backward.
If density is irrelevant then why is there no sound in a vacuum-regardless of temperature?

(I know these are poor examples but they support the facts.)

JimCasey

My Feedback: (1)

>>
If density is irrelevant then why is there no sound in a vacuum-regardless of temperature?

mtthomps

My Feedback: (2)

I have done the research, guys, and Mark is exactly correct. It has nothing to do with density. Water is a LIQUID, air is a GAS. They have different sound propagation rates as a property of the substance, not its density. Water is nearly incompressible, as a gas is not. Look on the web. There are a large number of "speed of sound" calculators. All they take for input is temp.

Tall Paul

The subject isn't what creates the speed of sound, it's how the speed of sound varies with altitude.
As ambient T decreases with altitude, the speed of sound follows suit..
As "density altitude" increases with temperature above ambient, the effect on the airplane is to degrade the airplane's performance.
See message #2.

StarskiPZ

-these both need to be considered. One law ( Boyle's ) states that P x Volume/T = A constant.
P=pressure, T=absolute temperature

Thus all aspects effect each other.

If you heat something the molecules 'move' faster, and so s.o.s is faster too. But the pressure increases and in the real atmosphere the air will 'spread out' and become less dense ( it is not kept in a sealed 'box' as per lab experiment.

As density drops, so does s.o.s.

Temperature has a major effect in real terms as we often fly in all weathers. Pressure? sea level is about 1 Bar ( 14.5psi ), and down to zero when you leave the earth's atmosphere!

mtthomps

My Feedback: (2)

You are not listening. Irrespective of pressure, sos is determined in a gas by the TEMPERATURE ONLY in a gas. IRRESPECTIVE OF PRESSURE. Pressure NOTHING to do with it. Density has nothing to do with it. Take a tank, pump out half the air, heat the gas back to room temp, and the speed of sound will be the same as to start with. PERIOD. The sound will be softer with a decrease in density, but it will not affect wave propagation velocity.

I fully realize that pressure drops with temperature decrease. This is not what I am talking about.

mtthomps

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Go to the following NASA url. On it you will find a "move the airplane" graphic. Set the output dropdown to "Speed of sound". Move the airplane up the scale. When the airplane gets close to the top of the scale, you will see the speed of sound climbing back up because the temp is climbing back up.

http://www.grc.nasa.gov/WWW/K-12/airplane/atmosi.html

mtthomps

My Feedback: (2)

The speed of sound at 28,400 feet is the same as 100,000 feet.

warbirdz1

Mark.....MTThomps.....You guys are correct as my understanding goes....Being an aircraft mech I see and talk with pilots most everyday about this topic in some form....most of all todays A/S indicators are electric/CRT/LCD...deriving its info either in analog form or digital form from a ADC/CADC (Air Data computer) from a TAT (Total Air temp) probe on the Fuselage in the fwd nose area depending on Manufacturer.....one of its main purposes in life(Amongst others) is to provide direct info to compute Mach Number....keep in mind "Density altitude" computation is temp/pressure compensated....where as Mach number is temp dependant only.......Above 20,000 ft as a rough measure as a plane increases altitude by 1000ft indicated airpeed drops by 2 %......so @ 21,000 if your at 350k indicated @ 37,000 ft you would be roughly 245k indicated.......also keeping in mind the lapse rate( rate @ which temp decreases) is roughly 3* drop per 1000 ft increase in altitude.....which influences density altitude......decreasing as well.....Bill.......

Johng

My Feedback: (4)

Jazzy and others -that table most definitely does not "tell all". It's just a list of standard numbers for the atmosphere. Each column is a list of increasing or decreasing numbers. That doesn't mean there is a direct relationship between one particular column and another.

If you can infer a relationship between SoS and density from that list, then I can just as easily asume SoS is related to pressure - and neither would be right. The only true physical relationship has been shown thru experimentation to be between Sos and temp. Any other assumptions I have seen here seem to be based on "common sense" feelings rather than science.

StarskiPZ

In a vacuum s.o.s = zero.

So in your air tank experiment, as you say, if you take half the air out, and keep the temperature the same, the s.o.s is unchanged??

If so, and you then removed another half of whats left ( leaving 1/4 ), and another ( leaving 1/8 ) etc.... at what point will the s.o.s drop?

Sound needs molecules / atoms to propergate which is why both temperature ( velocity / excitation of atoms ) AND the number ( density ) of particles are important.

This is also why the s.o.s is higher with increasing density of whatever the medium.

ie, s.o.s is faster in steel than in > water than > air > vacuum...

Please correct me if I'm wrong...