# How can one approximately guesstimate wave drag?

Wave drag is an especially high drag that affects supersonic vehicles above mach 1, but I've found it hard to find source materials to estimate wave drag. I'm looking at the transonic region till Mach 1.2 and so I'm looking to have an estimate about how I can design better for wave drag by estimating how it would affect my flight in the region mach 0.8 - 1.2.

• Welcome to Aviation.SE. Speeds up to Mach 1 are subsonic by definition and do not have wave drag. You might want to simplify your question to focus on one aspect. It requires several answers in its current form, and this site tends to like one at a time. – Pilothead Sep 18 '18 at 18:15
• Hey @Pilothead, thanks for the heads up. Thanks for welcoming me , and I have simplified the question and perhaps I'll add the other elements in another question. – Rajath Pai Sep 19 '18 at 1:28

Usually wave drag $$c_{d_w}$$ starts becoming relevant at the drag divergence Mach number $$M_{DD}$$, which is defined as

$$\frac{\partial c_{d_w}}{ \partial M}_{M=M_{DD}}=0.1 \tag{1}$$

Or in words, the Mach number at which the wave drag coefficient versus M has a gradient of 0.1

Lock$$^1$$ has derived an empirical formula that shows the development of $$c_{d_w}$$ after the critical Mach number, $$M_{cr}$$, which is the number at which the flow becomes locally supersonic on the wing:

$$c_{d_w} = 20(M-M_{cr})^4 \tag{2}$$

If we apply the definition of $$(1)$$ to $$(2)$$ we obtain:

$$M_{cr} = M_{DD} - \left(\frac{0.1}{80}\right)^{1/3} \tag{3}$$

As you can see, the value of $$M_{DD}$$, is a little bit higher than the value of $$M_{cr}$$. First you get local super sonic flow, but the drag does not increase rapidly, as you further increase the Mach number, the drag starts to increase significantly, and you reach $$M_{DD}$$. See this image, where $$M_{DD}$$ is denoted by $$M_{CDR}$$. Source

The value of $$M_{DD}$$ can be estimated using:

$$M_{DD} = \frac{K_A}{cos \Lambda} + \frac{t/c}{cos^2 \Lambda} +\frac{c_l}{cos ^3\Lambda} \tag{4}$$

With $$\Lambda$$ is the sweep angle, $$t/c$$ the relative thickness, $$c_l$$ the lift coefficient, and $$K_A$$ the airfoil technology factor (a correction factor denoting the quality of the airfoil).

So the workflow is as follows:

1. Estimate $$M_{DD}$$ using $$(4)$$
2. Derive $$M_{cr}$$ using $$(3)$$
3. Determine the development of $$c_{d_w}$$ using $$(2)$$.

$$^1$$ Hilton, W.F., High Speed Aerodynamics, Longmans, Green & Co., London, 1952, pp. 47-49