Critical Mach versus Altitude...
Joined: Sep 2000
Posts: 965
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From: Bielefeld, Germany
I am having a little difficulty understanding what you are proposing. Here is why.
Looking at the units, this is ((number) x Force) / (number x number x Area), i.e force per unit area. Let M be mass units, L be length units, T be time units. Force is then M x L / T^2; Area is L^2, so this comes down to M x L / T^2 x L^2, which is M / T^2 x L.
Whereas in the usual definition of c_L, which you quote as
c_L has no units: (M x L / T^2) / ( (M / L^3) x (L/T)^2 x L^2 ) all cancels out.
PBL
Originally Posted by HN39
c_L=1.3826*10^-4*W/(delta*M^2*S)
where W=weight (mass) in kg, delta=ratio of ambient to SLS pressure, M=Mach, S= (reference) wing area in m^2
where W=weight (mass) in kg, delta=ratio of ambient to SLS pressure, M=Mach, S= (reference) wing area in m^2
Whereas in the usual definition of c_L, which you quote as
Originally Posted by HN39
c_L ..... is commonly defined as LIFT/(q*S)
PBL
Joined: Jul 2009
Posts: 1,682
Likes: 0
From: France - mostly
PBL;
Yes, you're quite right. c_L is dimensionless. The formula interprets W as mass.
regards,
HN39
PM
The constant just after the equal sign is equal to 2*g/(rho*c^2), where:
g = acceleration of gravity at SL = 9.80665 m/s^2
rho = air density at SL std temp = 1.225 kg/m^3
c = speed of sound at SL std temp = 340.3 m/s
Yes, you're quite right. c_L is dimensionless. The formula interprets W as mass.
regards,
HN39
PM
The constant just after the equal sign is equal to 2*g/(rho*c^2), where:
g = acceleration of gravity at SL = 9.80665 m/s^2
rho = air density at SL std temp = 1.225 kg/m^3
c = speed of sound at SL std temp = 340.3 m/s
Last edited by HazelNuts39; 11th October 2010 at 13:51. Reason: Numerical values in PM
Joined: Sep 2000
Posts: 965
Likes: 110
From: Bielefeld, Germany
Originally Posted by HN39
The formula interprets W as mass, all units are accounted for in the number that precedes it, which has the dimension (in your notation) of L^2/M.
Terminology difference. Yes, it is now clear to me that your numbers are constants. However, I still have difficulty with equating weight with mass. Weight is to me still a force (opposed in the case of level flight to lift, and one which I feel clearly every time I pick up my suitcase), so still M x L / T^2.
PBL
Last edited by PBL; 11th October 2010 at 14:50. Reason: Clarification by HN39
Joined: Jun 2004
Posts: 178
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From: UK
An alternative (and perhaps simpler?) way into this one is to note that
q = 1/2*gamma*M^2*P
where P is staitc pressure, Hence:
c_L = weight/(1/2*gamma*M^2*P*S)
If you substitute P= delta*101325 Pa, weight = mass*9.80665 m/s^2 and gamma=1.4 you get HN39's formula.
In any event c_L (and hence alpha) increase as you cimb at constant Mach. Would Mcrit for a wing increase with alpha? I don't know but I would think it might.
q = 1/2*gamma*M^2*P
where P is staitc pressure, Hence:
c_L = weight/(1/2*gamma*M^2*P*S)
If you substitute P= delta*101325 Pa, weight = mass*9.80665 m/s^2 and gamma=1.4 you get HN39's formula.
In any event c_L (and hence alpha) increase as you cimb at constant Mach. Would Mcrit for a wing increase with alpha? I don't know but I would think it might.
Last edited by Rivet gun; 12th October 2010 at 08:23.
Joined: Jul 2009
Posts: 1,682
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From: France - mostly
AoA and altitude
This graph: Variation of AoA with altitude shows angle of attack at constant weight and Mach (0.65) for a typical new technology widebody airplane.
regards,
HN39
regards,
HN39
Joined: Dec 2006
Posts: 2,486
Likes: 8
From: The No Transgression Zone
The Prandtl relation and the more commonly used Karman Tsien have two main applications...
1. determine the lift slope curve dCl/dalpha
2. to find the highest incompressible Lift coefficient where the free stream
MN =1.00,...or Mcrit---usually in a graphical tabulation of some kind
1. determine the lift slope curve dCl/dalpha
2. to find the highest incompressible Lift coefficient where the free stream
MN =1.00,...or Mcrit---usually in a graphical tabulation of some kind
Last edited by Pugilistic Animus; 8th November 2010 at 12:45. Reason: replace MN with Cl---bold
