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THE MACH NUMBER

 

Information retrieved from : http://www.aerospaceweb.org/question/atmosphere/q0112.shtml

  
     
 

The present notes are associated with the Measurements page and linked with the preliminary design notes for the Head Up Display.   The purpose is to determine how to handle the Mach value in the context of AAC.

 
     
 

As outlined in the tables below, the Mach Number is a complex notion where air pressure and temperature play key roles.   In other words, the Mach Number is variable.   Here below are tables from aerospaceweb, with the first table being the reference for this topic, and on which the graphic is based.
   
As a matter of simplifications, we may consider one of the following options :

1

Consider a linear variation of the Mach number from 661.5 kts at 0 ft altitude to 587.5 kts at 365000 ft altitude - NOT RECOMMENDED

2

Consider an average value calculated on the sum of all values divided by their number (4392275 = 585.63 ~ 586 kts) illustrated by the lower pink line in the graph

3

Consider an average value midway of the extreme values  624.5 kts or 625 kts (re: the upper pink line in the graph)

However, considering most "fighter" planes have a ceiling of 65,000 ft or less, looking at the Mach number beyond this altitude only makes sense when considering extreme vehicle like the X-15.  Restricting ourselves to the 0-65000 ft altitude range triggers the following options :

4

Consider a linear variation of the Mach number from 661.5 kts at 0 ft altitude to 573.6 kts at 65,000 ft altitude

5

Consider an average value calculated on the sum of all values divided by their number (8400.1014 = 600.01 ~ 600 kts) illustrated by the lower blue line in the graph

6

Consider an average value midway of the extreme values : 617.55 kts or 618 kts (re: the upper blue line in the graph)

7

Consider a linear variation of the Mach number from 661.5 kts at 0 ft altitude to 573.6 kts at 65,000 ft altitude (same as #4) and then a constant value of 573.6 kts from 65,000 ft up to 365,000 ft (and beyond...) - illustrated by the green line in the graph - RECOMMENDED

   

Whichever the solution we choose is going to be a "cheat".  Maintaining a certain level of variation for the most common altitudes would provide a reasonable solution and the last suggestion provides a solution for the very few aircrafts with extreme peformances.

   
 

The tables below showing the speed for Mach 1.0 at various altitudes are extracted from Aerospaceweb.org, with the 1st table a copy of their imperial table, and the 2nd table a merge of both their imperial (5,000 ft increments) and metric table (2000 m increments)

 
Altitude : ft Speed : kts

0

661.5
5000 650.0
10000 638.3
15000 626.5
20000 614.3
25000 602.0
30000 589.4
35000 576.5
40000 573.6
45000 573.6
50000 573.6
55000 573.6
60000 573.6
65000 573.6
70000 575.2
Altitude : ft Speed : kts
75000 577.3
80000 579.2
85000 581.2
90000 583.2
95000 585.1
100000 587.1
105000 589.0
110000 594.1
115000 599.5
120000 604.8
125000 610.1
130000 615.3
135000 620.4
140000 625.6
145000 630.7
Altitude : ft Speed : kts
150000 635.7
155000 640.7
160000 641.1
165000 641.1
170000 639.8
175000 634.8
180000 629.7
185000 624.7
190000 619.5
195000 614.3
200000 609.2
205000 603.9
210000 598.6
215000 593.3
220000 588.0
Altitude : ft Speed : kts
225000 582.5
230000 577.1
235000 571.6
240000 567.4
245000 563.4
250000 559.4
255000 555.3
260000 551.2
265000 547.1
270000 543.0
275000 538.8
280000 534.6
285000 532.8
290000 532.8
295000 532.8
Altitude : ft Speed : kts
300000 533.1
305000 533.9
310000 534.7
315000 535.9
320000 538.6
325000 541.7
330000 547.2
335000 551.8
340000 557.1
345000 565.4
350000 573.5
355000 584.4
360000 586.0
365000 587.5
370000 589.1
Altitude
metre
Altitude
        ft
  Speed
   kts
  Speed
km/h
0 0   661.5   -
- 5000   650.0   -
2000 6562   646.4   1197.1
- 10000   638.3   -
4000 13123   631.0   1168.5
- 15000   626.5   -
6000 19685   515.1   1139.2
- 20000   614.3   -
- 25000   602.0   -
8000 26247   598.9   1109.2
- 30000   589.4   -
10000 32909   582.2   1078.3
- 35000   576.5   -
12000 39370   573.6   1062.3
- 40000   573.6   -
- 45000   573.6   -
14000 45932   573.6   1062.3
- 50000   573.6   -
16000 52493   573.6   1062.3
- 55000   573.6   -
18000 59055   573.6   1062.3
- 60000   573.6   -
- 65000   573.6   -
20000 65617   573.6   1062.3
- 70000   575.2   -
22000 72178   576.1   1067.0
- 75000   577.3   -
24000 78740   578.7   1071.8
- 80000   579.2   -
- 85000   581.2   -
26000 85302   581.3   1076.6
- 90000   583.2   -
28000 91864   583.9   1081.4
Altitude
metre
Altitude
        ft
  Speed
   kts
  Speed
km/h
- 95000   585.1   -
30000 98425   586.5   1086.2
- 100000   587.1   -
32000 104987   589.0   1090.9
- 105000   589.0   -
- 110000   594.1   -
34000 111549   595.8   1103.4
- 115000   599.5   -
36000 118110   602.8   1116.4
- 120000   604.8   -
38000 124672   609.7   1129.2
- 125000   610.1   -
- 130000   615.3   -
40000 131234   616.6   1141.9
- 135000   620.4   -
42000 137795   623.3   1154.4
- 140000   625.6   -
44000 144357   630.0   1166.8
- 145000   630.7   -
- 150000   635.7   -
46000 150919   636.6   1179.1
- 155000   640.7   -
48000 157480   641.1   1187.3
- 160000   641.1   -
50000 164042   641.1   1187.3
- 165000   641.1   -
- 170000   639.8   -
52000 170604   639.2   1183.7
- 175000   634.8   -
54000 177165   632.6   1171.5
- 180000   629.7   -
56000 183727   625.9   1159.2
- 185000   624.7   -
Altitude
metre
Altitude
        ft
  Speed
   kts
  Speed
km/h
- 190000   619.5   -
58000 190289   619.2   1146.8
- 195000   614.3   -
60000 196850   612.4   1134.3
- 200000   609.2   -
62000 203412   605.6   1121.6
- 205000   603.9   -
64000 209974   598.7   1108.8
- 210000   598.6   -
- 215000   593.3   -
66000 216535   591.7   1095.8
- 220000   588.0   -
68000 223097   584.6   1082.7
- 225000   582.5   -
70000 229659   577.4   1069.4
- 230000   577.1   997.0
- 235000   571.6   -
72000 236220   570.4   1056.4
- 240000   567.4   -
74000 242782   565.2   1046.7
- 245000   563.4   -
76000 249344   559.9   1036.9
- 250000   559.4   -
- 255000   555.3   -
78000 255905   554.6   1027.1
- 260000   551.2   -
80000 262467   549.2   1017.1
- 265000   547.1   -
82000 269029   543.8   1007.1
- 270000   543.0   -
- 275000   538.8   -
84000 275590   538.3   997.0
- 280000   534.6   -
Altitude
metre
Altitude
        ft
  Speed
   kts
  Speed
km/h
86000 282152   532.8   986.5
- 285000   532.8   -
88000 288714   532.8   986.5
- 290000   532.8   -
- 295000   532.8   -
90000 295276   532.8   986.5
- 300000   533.1   -
92000 301837   532.8   986.5
- 305000   533.9   -
94000 308399   533.9   988.8
- 310000   534.7   -
96000 314961   536.1   992.9
- 315000   535.9   -
- 320000   538.6   -
98000 321522   539.6   999.3
- 325000   541.7   -
100000 328084   544.3   1008.0
- 330000   547.2   -
102000 334646   550.4   1019.4
- 335000   551.8   -
- 340000   557.1   -
104000 341207   558.4   1034.1
- 345000   565.4   -
106000 347769   568.6   1053.0
- 350000   573.5   -
108000 354331   582.3   1078.4
- 355000   584.4   -
- 360000   586.0   -
110000 360892   584.6   1082.8
- 365000   587.5   -
112000 367454   587.0   1087.1
- 370000   589.1   -
114000 374016   589.3   1091.4