Author Topic: the compresion model (Read 772 times)

-ammo- · « **on:** October 20, 2001, 12:40:00 AM »

I have a question. This was brought up on RW the this evening and it has me wondering. We were in our P-47's diving on enemy AC in the TOD. One of the guys says "hey whats up with this, My AC is entering into compression and I am only doing 400 IAS." I think well dude, your TAS is pushing 550 so that isa the reason you are entering compression. I guiess I have more than 1 question--

1. We were at 25K or so when we started experiencing this. As we got lower the AC came out of compression, like it is supposed to. How fast was fast enough to trigger compression in real life?

2)Is the Critical Mach number only 400 IAS for the jug at 25K?

3) simply this.. Should TAS or IAS be used to gauge what speed compression starts?

funkedup · « **Reply #1 on:** October 20, 2001, 02:16:00 AM »

Mach number dictates when compressibility effects begin. Not TAS, not IAS. I forgot all the exact numbers, but last time we went over this the compressibility airspeeds for the AH Jug corresponded almost exactly with the critical Mach given in America's Hundred Thousand. If we had a search feature I'd give a link to the thread.

[ 10-20-2001: Message edited by: funkedup ]

Hobodog · « **Reply #2 on:** October 20, 2001, 09:50:00 PM »

http://www.hitechcreations.com/cgi-bin/ultimatebb.cgi?ubb=search

Zigrat · « **Reply #3 on:** October 20, 2001, 10:33:00 PM »

at 20k

sigma=.44 (d25k/dsl)
sqrt(sigma) = .66
TAS = 400/.66 = 600 mph

m=1 at 25k is 682.99 mph

so mcrit = .878

seems pretty reassonable. thats pretty high.

hitech · « **Reply #4 on:** October 20, 2001, 11:02:00 PM »

For those interested here are the tables we use.

Sigma
1.000000f, /* ALT 0.000000*/
0.985451f, /* ALT 500.000000*/
0.971064f, /* ALT 1000.000000*/
0.956838f, /* ALT 1500.000000*/
0.942772f, /* ALT 2000.000000*/
0.928865f, /* ALT 2500.000000*/
0.915116f, /* ALT 3000.000000*/
0.901523f, /* ALT 3500.000000*/
0.888085f, /* ALT 4000.000000*/
0.874800f, /* ALT 4500.000000*/
0.861668f, /* ALT 5000.000000*/
0.848688f, /* ALT 5500.000000*/
0.835857f, /* ALT 6000.000000*/
0.823176f, /* ALT 6500.000000*/
0.810642f, /* ALT 7000.000000*/
0.798255f, /* ALT 7500.000000*/
0.786013f, /* ALT 8000.000000*/
0.773915f, /* ALT 8500.000000*/
0.761961f, /* ALT 9000.000000*/
0.750148f, /* ALT 9500.000000*/
0.738475f, /* ALT 10000.000000*/
0.726943f, /* ALT 10500.000000*/
0.715548f, /* ALT 11000.000000*/
0.704291f, /* ALT 11500.000000*/
0.693169f, /* ALT 12000.000000*/
0.682183f, /* ALT 12500.000000*/
0.671330f, /* ALT 13000.000000*/
0.660610f, /* ALT 13500.000000*/
0.650021f, /* ALT 14000.000000*/
0.639562f, /* ALT 14500.000000*/
0.629233f, /* ALT 15000.000000*/
0.619032f, /* ALT 15500.000000*/
0.608958f, /* ALT 16000.000000*/
0.599010f, /* ALT 16500.000000*/
0.589186f, /* ALT 17000.000000*/
0.579486f, /* ALT 17500.000000*/
0.569909f, /* ALT 18000.000000*/
0.560454f, /* ALT 18500.000000*/
0.551119f, /* ALT 19000.000000*/
0.541903f, /* ALT 19500.000000*/
0.532806f, /* ALT 20000.000000*/
0.523826f, /* ALT 20500.000000*/
0.514963f, /* ALT 21000.000000*/
0.506214f, /* ALT 21500.000000*/
0.497580f, /* ALT 22000.000000*/
0.489059f, /* ALT 22500.000000*/
0.480650f, /* ALT 23000.000000*/
0.472352f, /* ALT 23500.000000*/
0.464164f, /* ALT 24000.000000*/
0.456085f, /* ALT 24500.000000*/
0.448114f, /* ALT 25000.000000*/
0.440250f, /* ALT 25500.000000*/
0.432492f, /* ALT 26000.000000*/
0.424839f, /* ALT 26500.000000*/
0.417290f, /* ALT 27000.000000*/
0.409845f, /* ALT 27500.000000*/
0.402501f, /* ALT 28000.000000*/
0.395258f, /* ALT 28500.000000*/
0.388116f, /* ALT 29000.000000*/
0.381073f, /* ALT 29500.000000*/
0.374127f, /* ALT 30000.000000*/
0.367280f, /* ALT 30500.000000*/
0.360528f, /* ALT 31000.000000*/
0.353872f, /* ALT 31500.000000*/
0.347310f, /* ALT 32000.000000*/
0.340842f, /* ALT 32500.000000*/
0.334466f, /* ALT 33000.000000*/
0.328182f, /* ALT 33500.000000*/
0.321989f, /* ALT 34000.000000*/
0.315885f, /* ALT 34500.000000*/
0.309870f, /* ALT 35000.000000*/
0.303944f, /* ALT 35500.000000*/
0.298104f, /* ALT 36000.000000*/
0.292351f, /* ALT 36500.000000*/
0.286683f, /* ALT 37000.000000*/
0.281100f, /* ALT 37500.000000*/
0.275600f, /* ALT 38000.000000*/
0.270183f, /* ALT 38500.000000*/
0.264847f, /* ALT 39000.000000*/
0.259593f, /* ALT 39500.000000*/
0.254419f, /* ALT 40000.000000*/
0.249324f, /* ALT 40500.000000*/
0.244307f, /* ALT 41000.000000*/
0.239368f, /* ALT 41500.000000*/
0.234506f, /* ALT 42000.000000*/
0.229720f, /* ALT 42500.000000*/
0.225008f, /* ALT 43000.000000*/
0.220372f, /* ALT 43500.000000*/
0.215808f, /* ALT 44000.000000*/
0.211317f, /* ALT 44500.000000*/
0.206898f, /* ALT 45000.000000*/
0.202550f, /* ALT 45500.000000*/
0.198273f, /* ALT 46000.000000*/
0.194065f, /* ALT 46500.000000*/
0.189925f, /* ALT 47000.000000*/
0.185853f, /* ALT 47500.000000*/
0.181849f, /* ALT 48000.000000*/
0.177911f, /* ALT 48500.000000*/
0.174038f, /* ALT 49000.000000*/
0.170230f /* ALT 49500.000000*/

SpeedOfSound Feet Per Sec

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*/

[ 10-20-2001: Message edited by: hitech ]

-ammo- · « **Reply #5 on:** October 20, 2001, 11:12:00 PM »

HT and zig, TY very much, however I understand none of that

Sancho · « **Reply #6 on:** October 20, 2001, 11:38:00 PM »

What does the sigma number mean?

funkedup · « **Reply #7 on:** October 21, 2001, 12:07:00 AM »

Sigma is the air density at a given altitude divided by the air density at sea level.

Assuming ideal behavior of the airspeed indicator, TAS is equal to IAS divided by the square root of sigma.

Mach number is TAS divided by the speed of sound.

Critical Mach is the Mach number at which local airflow at some point on the wing (or another part of the airplane) reaches sonic speed. At this Mach number drag begins to increase drastically, shock waves form, buffeting can occur, basically bad things start to happen on a WWII prop plane.

[ 10-21-2001: Message edited by: funkedup ]

funkedup · « **Reply #8 on:** October 21, 2001, 12:17:00 AM »

What Zig means is that 400 IAS at 25k is a Mach number of 0.878. This is quite high for a prop fighter. My books are in storage right now so I can't look it up, but I believe the the critical Mach for the P-47 was 0.82 or 0.83. So 400 IAS at 25k is well beyond critical Mach and you should expect bad things to be happening.

For comparison the P-38 critical Mach was something like 0.70.

(PS Using HT's official numbers, 400 mph IAS at 25k' is Mach 0.862)

[ 10-21-2001: Message edited by: funkedup ]

gripen · « **Reply #9 on:** October 21, 2001, 04:37:00 AM »

Hm... First it should be noted we must know conditions (pressure and temperature) at given altitude to calculate exact mach number. Anyway in the most cases standard conditions are enough. It should be also noted that depending on plane the IAS values must be also corrected.

Some formulas

Then it seems that people are mixing terms here. The critical mach number is the mach value where the compressebility effects (buffeting, tuck under or what ever) start, this value depends on plane and it stays pretty constant at all altitudes at given g load (the TAS and IAS value for the critical mach number decreases when the altitude raises while the mach value is constant). The max terminal velocity mach number of the plane is the max mach number which the given plane can reach in the terminal velocity at given altitude and this value raises when the altitude raises.

In the case of the P-47 the critical mach number was about 0,76 and at high altitude the max terminal velocity of the plane was over mach 0,8, so the P-47 could reach compressebility area in the dive at high altitude and this caused things like buffeting and elevator lock up. But when the plane reaches lower altitude where the air was densier and warmer, then the max terminal velocity is lower than the critical mach number and the plane comes out of compressebility and elevator control comes back making pull out possible.

The dive brakes did not change critical mach number but they added a lot of drag to avoid compressebility and they also changed the pitch moment so that the plane came out of dive or could be pulled out. In the case of the P-38 the dive brakes gave 3g pull out at 10k and about 1g at 30k.

See this

and this

and this

and finaly this

gripen

[ 10-21-2001: Message edited by: gripen ]