Maximum Theoretical and Practical L/D - Ratio vs Mach Number

[KJ_Lesnick]

I'm wondering what the maximum theoretical L/D ratio and the maximum practical L/D ratio achievable by an airfoil or airplane/airfoil combination at the following Mach numbers are...

SUBSONIC
Mach 0.70
Mach 0.80
Mach 0.90

SUPERSONIC
Mach 2.0
Mach 2.5
Mach 2.7
Mach 3.0
Mach 3.2
Mach 4.0

HYPERSONIC
Mach 5.0
Mach 6.0
Mach 7.0
Mach 8.0
Mach 9.0
Mach 10.0
Mach 12.0

How much of a gain would you say laminar flow control (if it was achievable) would improve such an optimal practical airfoil, airfoil/aircraft-combination at those mach numbers?


KJ Lesnick
BTW: Also does the Breguet-Range equation *actually* equate to a plane having an actually higher L/D ratio as a result of mach number increased?

 

[Simon666]

I'm wondering what the maximum theoretical L/D ratio and the maximum practical L/D ratio achievable by an airfoil or airplane/airfoil combination at the following Mach numbers are...

There's no real theoretically known maximum L/D ratio, although many theories with (vast) simplifications like Newtonian theory derive some formulas:

http://www.aerospaceweb.org/design/waverider/theory.shtml#newtonian

Kuchemann also analyzed the maximum L/D trend with mach number and formulated the general empirical relationship for practical maximum attainable L/D:

(l/d)max = 4 * (M+3) / M

with M the mach number.

 

[KJ_Lesnick]

Simon666,

I'm not sure how accurate Kuchemann's formula was...

The B2707-100 while primarily a Mach 2.7 design was tested up to Mach 3.0 and at those speeds they were able to get L/D ratios above 9:1...


KJ

 

[overscan (PaulMM)]

KJ please look up the meaning of "general empirical relationship". Its not some kind of immutable law.

Having said that l/d ratio on Boeing 2707-100 was 8.2 at Mach 2.0, according to some NASA studies I have. Where did the 9 figure come from?

 

[Simon666]

KJ please look up the meaning of "general empirical relationship". Its not some kind of immutable law.

Having said that l/d ratio on Boeing 2707-100 was 8.2 at Mach 2.0, according to some NASA studies I have. Where did the 9 figure come from?

Besides, even if you plug in the mach numbers he gave in that elementary math, the l/d claimed is still below the l/d max (=4*6/3=12). :

 

[overscan (PaulMM)]

Erm, thats 8 actually

 

[KJ_Lesnick]

Overscan,

KJ please look up the meaning of "general empirical relationship". Its not some kind of immutable law.

I stand corrected

Having said that l/d ratio on Boeing 2707-100 was 8.2 at Mach 2.0, according to some NASA studies I have. Where did the 9 figure come from?

Are you sure? From what I read, at Mach 2.7 the L/D ratio was 8.2 or 8.3 -- I'm pretty sure of this because it's L/D ratio at cruise was superior to the L-2000 which produced an L/D ratio of 8.0 @ Mach 3.0...

Regardless, even though the B-2707-100 was not ultimately designed for Mach 3 capability, they did however conduct some tests on the design (Shortly after the B-2707-100 design came into being) up to Mach 3.0, and to the best of my knowledge, L/D ratios went above 9.0 during those tests. From what I remember Boeing decided to go with Mach 2.7 because it allowed a simpler inlet-design, produced lower skin temperatures and made for less maintenance.


KJ

 

[Simon666]

Erm, thats 8 actually

I could bang myself on the head with a hammer for that one but I'm afraid it might only make things worse.