#### GL-P

##### Well-Known Member
Is this true?

I heard that boattials on supersonic rockets actually make drag worse because of wave drag.

Thanks

#### illini

##### Well-Known Member
According to Barnes McCormick in "Aerodynamics, Aeronautics, and Flight Mechanics," the supersonic base drag coefficient based on the base area must satisfy the inequality:

Cdb < 2/gamma/M^2

That is, the supersonic base drag coefficient is less than 2 divided by the constant gamma (gamma = 1.4 for air) divided by the Mach number squared. According to McCormick, there is no accepted method available for calculating Cdb, so a conservative estimate is to make the inequality an equality. i.e., Cdb = 2/gamma/M^2. So, for example, at M = 1, Cdb ~ 1.42. However, this is quite possibly way too high an estimate. It is, after all, only an upper bound according to McCormick.

Now, note what's in italics above. This drag coefficient is based on the base area. That is, the base drag is:

Db = 1/2 * density * velocity^2 * Cdb * Ab

So if the coefficient is constant (it isn't, but let's pretend), then the base drag is reduced linearly with base area. Bottom line, a boat tail makes sense even in supersonic flow.

#### GL-P

##### Well-Known Member
k, thanks, don't remember where I saw that info on boattails.

#### DynaSoar

##### Well-Known Member
To follow up, does boat tail shape a difference for trans/supersonic CD? Conical noses are better, how about conical vs. other tails?

#### Stymye

##### Well-Known Member
from what I've read ,an angle between 5 and 10 degrees is ideal
anything greater and seperation can occur on the boat tail.

I also understand that recessing the motor into the boat tail will further reduce base drag

so conical seems like a better choice

#### Chilly

##### Well-Known Member
I'm scratching out my own designs for a mach-buster, probably 38mm J-powered.
The challenge is that I want to do it with something other than minimum-diameter airframes, so it can have the strength of thru-the-wall fins. It seems the only efficient way to do that is with a boat tail and a long conical nose.
So is the benefit of boat-tailing rockets similar to the area rule for aircraft? For that matter, would using transitions to create a "coke-bottle" shape improve transonic performance in a rocket?

#### illini

##### Well-Known Member
Originally posted by DynaSoar
To follow up, does boat tail shape a difference for trans/supersonic CD? Conical noses are better, how about conical vs. other tails?

Been nastily busy lately, but see questions piling up so will try to give a quick response.

Will shape matter? Yes. Shape always matters. Now the harder question: what's the *best* shape for a boat tail? And even harder: how *much* will it matter? Good questions. Haven't had time to dig into it so I'll just have to fall back on McCormick for now: predicting the base drag coefficient in supersonic flow is hard. But whatever it is, it is referenced to base area. My gut feel is that you don't want to reduce area so fast that you risk separation...the point of separation becomes, in effect, your base. So I think I'd come down on the side of a gradual conical boat tail down to motor diameter. That's shootin' from the hip. Could be wrong.

#### illini

##### Well-Known Member
Originally posted by Chilly
So is the benefit of boat-tailing rockets similar to the area rule for aircraft? For that matter, would using transitions to create a "coke-bottle" shape improve transonic performance in a rocket?

Two different things, but both are relevant to a Mach buster. Boat-tailing has to do with reducing the base drag. Area ruling (not just for aircraft!) has to do with reducing wave drag.

Let's review base drag first. Base drag has to do with that nasty low pressure area at the base of your rocket sucking the flow from the sides around into nasty drag-producing vortices (kind of fond of the word "nasty" today for some reason). If the base is small, then the low pressure region is small and the drag will be less. However, the big gotcha is that if you try to reduce the area from the BT to base too quickly, the flow will separate before you reach the base and you're back to square 1. Beware separation! In another thread I posted a link to an article on the classic sphere in a wind tunnel experiment (I think it was the "flat plate" thread). Illustrates effects of viscosity and separation on drag very nicely.

Wave drag is due to shocks and shocklets forming. Shocks are basically viscous layers with very steep velocity gradients...a nasty source of drag in itself. Even worse, when shocks are curved they produce rotational flow (i.e., vortices) behind the shocks. Shocks are inevitable in trans/supersonic flow (strike THREE!). HOWEVER, there are ways to lessen their impact (i.e., lower the wave drag). I alluded to one of these in another thread somewhere: many weak shocks is usually better than one strong one (witness the mixed compression inlet), and oblique shocks are weaker than "normal" shocks (90 degrees to the direction of the flow). The area rule basically says sudden changes in cross sectional area result in stronger shocks and, therefore, more wave drag. If the rate of change of cross sectional area is smooth and gradual, life is good. If there is a sudden jump in area (e.g., at the wing or fin leading edge without reducing body area), life is bad.

#### GL-P

##### Well-Known Member
Okay, there's seperation with too short of a boattail.

This will probably be a bad boattail:

Front Diameter: 1 inch
Rear Diameter: 0.5 inch
Length : 0.25 inch

Forget the boattail or use a differently shaped boattail (Von Kaarman?)

Thanks!

#### illini

##### Well-Known Member
You have a 45 degree angle on each side. I'd say that's waaaaay too steep. The numbers tossed around here are on the order of 5 to 10 degrees. I think conical should be fine as long as the slope is more in line with 5 to 10 degrees.

#### GL-P

##### Well-Known Member
I figured that much. It's the best that I can do because I am limited in length on the boattail. (I'm using the motor nozzle as a boattail)

#### Todd Knight

##### Well-Known Member
Originally posted by Chilly
I'm scratching out my own designs for a mach-buster, probably 38mm J-powered.
The challenge is that I want to do it with something other than minimum-diameter airframes, so it can have the strength of thru-the-wall fins. It seems the only efficient way to do that is with a boat tail and a long conical nose.
So is the benefit of boat-tailing rockets similar to the area rule for aircraft? For that matter, would using transitions to create a "coke-bottle" shape improve transonic performance in a rocket?

Weight is the big issue. On lower impulse motors, including 38mm Js, any changes like you are talking about add weight. Even the Al boat-tails add a relatively significant amount of weight. Think short span fins that are thin with long cord. Look at ShadowAero designs as they are optimized for this type of profile.

Also, contact Mark Mazzon, one of our local TAPS. He lives in Sunbury and has been rolling his own FG and CF tubes and has a pretty unique way of surface mounting fins. We have been getting together once or twice a month to make EX and I am sure he would impart some wisdom on your design.

#### Jerry Irvine

##### Well-Known Member
Originally posted by illini
You have a 45 degree angle on each side. I'd say that's waaaaay too steep. The numbers tossed around here are on the order of 5 to 10 degrees. I think conical should be fine as long as the slope is more in line with 5 to 10 degrees.

7 degrees (each side).

I have been doing rockets a while and supersonic rockets longer than almost all.

I have flown hypersonic rockets.

Jerry

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