Author Topic: Question about Mach Numbers (Read 1394 times)

Traveler · « **on:** November 22, 2006, 01:50:45 PM »

The speed of sound in dry air is given approximately by

Hyper Physics

Because the speed of a sound in the air is determined by the air itself. It is not dependent upon the sound amplitude, frequency or wavelength and the formula for determining the speed of sound in air is dependent on a constant with only one variable; that being air temperature expressed as Celsius for the altitude.

The speed of sound in dry air is given approximately by

V sound in air = 331.4 + 0.6Tc m/s

I was flying an ME 262 at 25K with a E6B true airspeed of 525 mph which yielded a .76 of Mach. A simple matter of solving for X to determine the outside air temp at 25K.

.76 requires a speed of sound to be around 700 mph which requires an outside air temp of about -31 C or -24 F to attain.

That is great for 25K, so I did it again at 10K , 5K and 20 feet above sea level. The air temptrue at each of these was the same as 25K.

That is not an accurate model for the speed of sound in any aircraft.

hitech · « **Reply #1 on:** November 22, 2006, 01:55:27 PM »

AH's Mach conversion table.

Speed of sound in fps.

1116.89f, /* ALT 0.000000*/
1114.97f, /* ALT 500.000000*/
1113.05f, /* ALT 1000.000000*/
1111.12f, /* ALT 1500.000000*/
1109.19f, /* ALT 2000.000000*/
1107.25f, /* ALT 2500.000000*/
1105.31f, /* ALT 3000.000000*/
1103.37f, /* ALT 3500.000000*/
1101.43f, /* ALT 4000.000000*/
1099.48f, /* ALT 4500.000000*/
1097.53f, /* ALT 5000.000000*/
1095.57f, /* ALT 5500.000000*/
1093.61f, /* ALT 6000.000000*/
1091.65f, /* ALT 6500.000000*/
1089.68f, /* ALT 7000.000000*/
1087.71f, /* ALT 7500.000000*/
1085.74f, /* ALT 8000.000000*/
1083.76f, /* ALT 8500.000000*/
1081.78f, /* ALT 9000.000000*/
1079.80f, /* ALT 9500.000000*/
1077.81f, /* ALT 10000.000000*/
1075.82f, /* ALT 10500.000000*/
1073.83f, /* ALT 11000.000000*/
1071.83f, /* ALT 11500.000000*/
1069.83f, /* ALT 12000.000000*/
1067.82f, /* ALT 12500.000000*/
1065.81f, /* ALT 13000.000000*/
1063.80f, /* ALT 13500.000000*/
1061.78f, /* ALT 14000.000000*/
1059.76f, /* ALT 14500.000000*/
1057.73f, /* ALT 15000.000000*/
1055.70f, /* ALT 15500.000000*/
1053.67f, /* ALT 16000.000000*/
1051.63f, /* ALT 16500.000000*/
1049.59f, /* ALT 17000.000000*/
1047.55f, /* ALT 17500.000000*/
1045.50f, /* ALT 18000.000000*/
1043.45f, /* ALT 18500.000000*/
1041.39f, /* ALT 19000.000000*/
1039.33f, /* ALT 19500.000000*/
1037.26f, /* ALT 20000.000000*/
1035.19f, /* ALT 20500.000000*/
1033.12f, /* ALT 21000.000000*/
1031.04f, /* ALT 21500.000000*/
1028.96f, /* ALT 22000.000000*/
1026.88f, /* ALT 22500.000000*/
1024.79f, /* ALT 23000.000000*/
1022.69f, /* ALT 23500.000000*/
1020.59f, /* ALT 24000.000000*/
1018.49f, /* ALT 24500.000000*/
1016.38f, /* ALT 25000.000000*/
1014.27f, /* ALT 25500.000000*/
1012.15f, /* ALT 26000.000000*/
1010.03f, /* ALT 26500.000000*/
1007.91f, /* ALT 27000.000000*/
1005.78f, /* ALT 27500.000000*/
1003.64f, /* ALT 28000.000000*/
1001.51f, /* ALT 28500.000000*/
999.362f, /* ALT 29000.000000*/
997.251f, /* ALT 29500.000000*/
995.062f, /* ALT 30000.000000*/
992.905f, /* ALT 30500.000000*/
990.743f, /* ALT 31000.000000*/
988.577f, /* ALT 31500.000000*/
986.405f, /* ALT 32000.000000*/
984.229f, /* ALT 32500.000000*/
982.048f, /* ALT 33000.000000*/
979.862f, /* ALT 33500.000000*/
977.672f, /* ALT 34000.000000*/
975.476f, /* ALT 34500.000000*/
973.276f, /* ALT 35000.000000*/
971.070f, /* ALT 35500.000000*/
968.859f, /* ALT 36000.000000*/
968.859f, /* ALT 36500.000000*/
968.859f, /* ALT 37000.000000*/
968.859f, /* ALT 37500.000000*/
968.859f, /* ALT 38000.000000*/
968.859f, /* ALT 38500.000000*/
968.859f, /* ALT 39000.000000*/
968.859f, /* ALT 39500.000000*/
968.859f, /* ALT 40000.000000*/
968.859f, /* ALT 40500.000000*/
968.859f, /* ALT 41000.000000*/
968.859f, /* ALT 41500.000000*/
968.859f, /* ALT 42000.000000*/
968.859f, /* ALT 42500.000000*/
968.859f, /* ALT 43000.000000*/
968.859f, /* ALT 43500.000000*/
968.859f, /* ALT 44000.000000*/
968.859f, /* ALT 44500.000000*/
968.859f, /* ALT 45000.000000*/
968.859f, /* ALT 45500.000000*/
968.859f, /* ALT 46000.000000*/
968.859f, /* ALT 46500.000000*/
968.859f, /* ALT 47000.000000*/
968.859f, /* ALT 47500.000000*/
968.859f, /* ALT 48000.000000*/
968.859f, /* ALT 48500.000000*/
968.859f, /* ALT 49000.000000*/
968.859f /* ALT 49500.000000*/

JB88 · « **Reply #2 on:** November 22, 2006, 02:02:59 PM »

Traveler · « **Reply #3 on:** November 22, 2006, 02:05:03 PM »

so in the game it's table driven, but the table was based on a formula, right? I'm, just saying that the air temp woud not be the same at each altitude. The fps is that feet per second, or frames per second?

thanks

Traveler · « **Reply #4 on:** November 22, 2006, 02:30:18 PM »

Quote

Originally posted by hitech
AH's Mach conversion table.

Speed of sound in fps.

1116.89f, /* ALT 0.000000*/
1097.53f, /* ALT 5000.000000*/
1077.81f, /* ALT 10000.000000*/
1016.38f, /* ALT 25000.000000*/

1116.89f,/* Alt 0.000000*/ yields 762.5588812800001 mph at an air temp of 58F
1097.53f, /* ALT 5000.000000*/ 749.3408025600001 mph 40 F
1077.81f, /* ALT 10000.000000*/ 735.87693312 mph 23 F
1016.38f, /* ALT 25000.000000*/ 693.93547776 mph -32.5 F

That's the number I should have gotten based on the table, however, on the E6B, that's not what I got. Running at each altitued for 3 minutes level flight. The number I got were very different. Also, it appears that the ME262, never stops excelerating at any altitude and would continue to excelerate until it runs out of fuel. There must have been an airspeed restriction to prefent airframe damage, no?

dtango · « **Reply #5 on:** November 22, 2006, 02:46:13 PM »

Traveler:

The me-262 is not supersonic. I think that's your point of confusion with this.

Tango, XO
412th FS Braunco Mustangs

WilldCrd · « **Reply #6 on:** November 22, 2006, 02:51:09 PM »

i can apreciate your stiving for realisim however at some point the devolopers have to stop and use a table that models something like this as close as game mechanics allow. i may be wrong BUT, i beleive its a matter of players pc's over a wide spectrum to be able to do all the extra calculations to provide super uber realism such as temp difference's at altitude with direct correlation to its affects on a particular A/C movement thru the air.

Kuhn · « **Reply #7 on:** November 22, 2006, 02:57:03 PM »

Quote

Originally posted by JB88

Me too!!

dtango · « **Reply #8 on:** November 22, 2006, 03:00:58 PM »

Quote

Originally posted by WilldCrd
i can apreciate your stiving for realisim however at some point the devolopers have to stop and use a table that models something like this as close as game mechanics allow. i may be wrong BUT, i beleive its a matter of players pc's over a wide spectrum to be able to do all the extra calculations to provide super uber realism such as temp difference's at altitude with direct correlation to its affects on a particular A/C movement thru the air.

Ahh willdCrd, the kicker is that HTC does use air temp differences at alt to correlate to particular a/c movements thru the air. That's what the table HT shows implies.

Don't confuse the use of tables vs. some other way of calculating as less realism. Nothing could be further from the truth

.

Tango, XO
412th FS Braunco Mustangs

WilldCrd · « **Reply #9 on:** November 22, 2006, 03:35:02 PM »

hmm well i didnt know he did.
For the original poster you CAN get a 262 supersonic, i know cause i've done it!!

was in a dive, had no wings or tail and probly missing some other non-important stuff but, by-god was supersonic. It was the sudden STOP from supersonic that kinda ruined the whole experience:huh

Traveler · « **Reply #10 on:** November 22, 2006, 03:53:59 PM »

Quote

Originally posted by dtango
Traveler:

The me-262 is not supersonic. I think that's your point of confusion with this.

Tango, XO
412th FS Braunco Mustangs

I know that, Mach is a percentage of the speed of sound. Sound travels at different speeds at different altitudes depending on the air tempture. Supersonic refers to aifcraft that travel faster then the speed of sound.

I was just pointing out that the E6B gives the aircraft speed as a indicated airspeed, true airspeed, ground speed and the Mach number.

When I tested the 262 at see level it yielded a Mach of .67 for a true airspeed of 505 mph. That translated to an outside air temp at see level of -24 F. What I should have gotten was a air temp of 58 F.

that's what I questioned. To have gotten the true airspeeds and the Mach numbers that I received ment that something was wrong.

True air speed increases as you climb. The speed of sound decreases as you climb. The outside air temperature generally decreases as you climb. But according to the numbers yielded by the E6B for the test run I made at sea level. The outside air temperature would have had to have been -24 F.

dtango · « **Reply #11 on:** November 22, 2006, 04:38:05 PM »

Traveler:

The equation you have is for the speed of sound. You can't plug in the 262 velocity into the equation and then get the resulting temperature.

For the equation to yield the temperature the number you have to put in is the speed of sound. So if I take your 262 level speed figures showing 505 mph at mach .67, Mach 1 would then be 753 mph meaning air temp is 48F SL not the 24F that you got.

Tango, XO
412th FS Braunco Mustangs

calan · « **Reply #12 on:** November 22, 2006, 05:30:51 PM »

Quote

Originally posted by Traveler
Sound travels at different speeds at different altitudes depending on the air tempture.

I thought it had as much (or more) to do with air density....

Traveler · « **Reply #13 on:** November 22, 2006, 05:43:12 PM »

Quote

Originally posted by calan
I thought it had as much (or more) to do with air density....

Then you thought wrong, go to Google search speed of sound.

Traveler · « **Reply #14 on:** November 22, 2006, 05:48:25 PM »

Quote

Originally posted by dtango
Traveler:

The equation you have is for the speed of sound. You can't plug in the 262 velocity into the equation and then get the resulting temperature.

For the equation to yield the temperature the number you have to put in is the speed of sound. So if I take your 262 level speed figures showing 505 mph at mach .67, Mach 1 would then be 753 mph meaning air temp is 48F SL not the 24F that you got.

Tango, XO
412th FS Braunco Mustangs

You are correct about "you can't plug in the 262 volocity into the equation" however, you take true airspeed and calculate for velocity. Search Google for speed of sound. The forumla is there.