# math question

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#### bobby_hamill

##### Well-Known Member
working on a transition for a build

transition top outside diameter = 2.14 inches

transition bottom outside diameter = 4.024 inches

It does not tell me how long the transition is only that it is a 30:1 transition

With these known measurement how long would the transition be ?

Thanks

Bobby

working on a transition for a build

transition top outside diameter = 2.14 inches

transition bottom outside diameter = 4.024 inches

It does not tell me how long the transition is only that it is a 30:1 transition

With these known measurement how long would the transition be ?

Thanks

Bobby
Subtract the radii of the two OD's. Multiply that by 30. Gives 28.26 inches. Does that look right it you scale off the drawing?

What is the rocket? Where and how does it say 30:1?

Generically here are the equations for transitions/shrouds...

Maybe the 30:1 is R2 to R1...then you would have to work backwards in the equations to figure out L.

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It is for an Aerobee 300 Sparrow & payload section launched at Churchill Canada
The Aerobee 300A is the same as the Aerobee 300
Difference is the
Aerobee 300 uses the 3 fin Aerobee 150 motor
Aerobee 300A uses the 4 fin Aerobee 150A motor

My downscale uses
4.024 diameter for the 3 fin Aerobee 150 motor
Sparrow Motor uses a 2.14 diameter
The payload cylinder and cone are 1.72 diameter

The Aerobee 300 flight 6.10 GA has 2 transitions
1 transition between the Aerobee 150 motor and the Sparrow Motor
2 transition also called a "Payload Adapter" is between the Sparrow Motor
and the The payload cylinder and cone

The 30:1 transition cone is circled in red in the photo attached

Subtract the radii of the two OD's. Multiply that by 30. Gives 28.26 inches. Does that look right it you scale off the drawing?
2.14OD = r of .3405916
4.0246OC = r of .64044
.64044 - .3405916 = .29984
.29984 * 30 = 8.99

Not arguing, trying to clarify. 8" transition is way better than 30"...

According to Peter's information, the Aerobee 300 shroud angle is 14.5° from vertical.

Given the 15.0" & 8.0" tube sizes, the length of the full scale transition would be 13.53". You can scale that with your other measurements.

The rotation angle in MarsLander's drawing above is 97.8°

15 "diameter for the 3 fin Aerobee 150 motor
Sparrow Motor uses a 8 " diameter
The payload cylinder and cone are 6.5 " diameter

Full size measurements

actual rocket at Churchill

Post 4 from above is everything in the attached photo that is white including payload section

here is a close up of the text on the sparrow motor

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IF you assume that your rocket is ~1/4 scale as 8" forward tube is your 2.14 tube, the math works out like this...

8" / 2.14 = 3.6193

Scale the 13.53" long transition / 3.7383 = 3.6193 long transition on your rocket.

The math becomes:

If you decide to scale from the 15" to the 4.024, your scale factor is 1/3.7276.

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The 30:1 is obviously incorrect information from looking at the pictures.

According to Peter's information, the Aerobee 300 shroud angle is 14.5° from vertical.
Either Peter's information is off, or my math is off. Angle in my math (sin phi) is 25.2.

Here is 25 vs 14.5....what do you guys think?

Looks closer to 14.5 than 25!

The cone on the Sparrow tail was both an interstage adapter and a tail nozzle.
So the "30:1" figure I believe is not a reference to the dimensions but the exhaust gas expansion.
JMHO.

Either Peter's information is off, or my math is off. Angle in my math (sin phi) is 25.2.

Here is 25 vs 14.5....what do you guys think?

View attachment 620482

I drew that up (based on his drawing) about 25 years ago. IIRC, Peter only gave the angle in ROTW, I'm pretty sure I calculated the hypotenuse.

½(15"-8")÷tan14.5°=13.53"

I'll look to see if I still have his drawing, but it worked perfectly for the transition test shroud I cut from posterboard.

I am gonna try and get in contact with the Canadian NRC or CISTI library to get some documents on these early
1958-1959-1960 Aerobee 300 flights at Churchill

Aerobee-300 22.10.1958 * FC AA10.01
Aerobee-300 25.10.1958 * FC AA10.02
Aerobee-300 30.11.1958 * FC ABM10.200
Aerobee-300 01.12.1958 *F FC NN10.001
Aerobee-300 03.12.1958 * FC NN10.002
Aerobee-300 25.10.1959 * FC AA10.184C
Aerobee-300 28.10.1959 * FC AA10.185C
Aerobee-300 06.11.1959 * FC AA10.187C
Aerobee-300 14.11.1959 * FC AA10.165C
Aerobee-300 22.11.1959 *F FC AA10.186C

6.01 UI 16 March 1960 Churchill
6.02 UI 15 June 1960 Churchill
6.10 GA 28 July 1964 Churchill

I am gonna try and get in contact with the Canadian NRC or CISTI library to get some documents on these early
1958-1959-1960 Aerobee 300 flights at Churchill

I'll be on the edge of my seat.

Since those first 5 flights were part of the I.G.Y. research, they may be documented in the "International Geophysical Year Collection" within the NAS Archives. I've found sections that look like there may be good info, but little of it is online.

I am hoping that the early launches of the Aerobee 300 didn't have the second transition between the
Sparrow motor and the payload section like the Estes version was modeled from

NAS = National Aerospace Archives ?

Found it = National Academy of Sciences

I am hoping that the early launches of the Aerobee 300 didn't have the second transition between the
Sparrow motor and the payload section like the Estes version was modeled from

Me, too! Peter said the early flights had full 8" payloads.

NAS = National Aerospace Archives ?

Sorry I didn't clarify, National Academy of Sciences. They have 153 feet of IGY archives.

153 feet I would need to bring a tent and a case of sim cards for my Nikon Camera

My Dad and his dad were sheetmetal workers at a large firm. I worked there for 8 years after I got out of college. In the area where I worked there was a large desk where different guys would layout what they were assigned. There was a large roll of paper that they would use. I was amazed watching them lay things out. Things like going from a square end to a round end while making a bend. I think picking up a sheetmetal layout book would be very useful for rocket building.

My Dad and his dad were sheetmetal workers at a large firm. I worked there for 8 years after I got out of college. In the area where I worked there was a large desk where different guys would layout what they were assigned. There was a large roll of paper that they would use. I was amazed watching them lay things out. Things like going from a square end to a round end while making a bend. I think picking up a sheetmetal layout book would be very useful for rocket building.

It would, actually. Most of the stuff from Joe Kaberlein is pretty good. I'm sure there are others that are fine.

I run a sheet metal shop and we normally take care of transitions and odd fittings with software these days. We used to have three large wood tables for hand/math layouts, now we just have a plasma.

We normally build kind of large stuff (think duct large enough you can walk through it, or drive in it). I've built a couple of rocket transitions, but my minimum diameter for metal solutions is around 3".

I'll look to see if I still have his drawing, but it worked perfectly for the transition test shroud I cut from posterboard.
You are correct. I corrected the math above. Should be an accurate shroud calculation now:

The shop where Dad worked did big stuff for paper mills, taconite plants, power plants, etc. I was always amazed at what the guys could layout by hand. I still have my Dad's layout books. And there are some good YouTube videos about doing layouts.

You are correct. I corrected the math above. Should be an accurate shroud calculation now:

View attachment 620558
Forget the angles. The angles weren't the question.

2.14OD = r of .3405916
2.14" Outside Diameter, not circumference. R1=1.07".
4.024" OD gives R2=2.012".
ΔR=0.942".
30ΔR=28.26", which is obviously not the correct length. But that's been covered.

3.0ΔR=2.826", which may be just about right (transition length lying somewhere between the two diameters). So perhaps it's a simple misprint.

Let's suppose that's the answer, then get back to angles. The slope would then be 3ΔR ÷ R = 3. Thus, the angle from vertical is cot-13 ≈ 18.4°. Post 14 shows it as 16°, which may be within the achievable precision from 18.4° given both the graininess of the photo and any perspective effects.

That's my answer, and I'm sticking to it.

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Thinking back, I recall how our teacher would say during our lessons: 'Working on a transition for a build. To calculate the length of the transition, you can use the ratio of the diameters given. Since the transition is described as a 30:1 transition, it means that the diameter at the top is 1/30th of the diameter at the bottom.
P.S Just a reminder in case I've forgotten some details. Because I even used such a service https://essays.edubirdie.com/math to search for the answer, but unfortunately, earlier they didn't give me an exact answer to this question.
working on a transition for a build

transition top outside diameter = 2.14 inches

transition bottom outside diameter = 4.024 inches

It does not tell me how long the transition is only that it is a 30:1 transition

With these known measurement how long would the transition be ?

Thanks

Last edited:
Thinking back, I recall how our teacher would say during our lessons: 'Working on a transition for a build. To calculate the length of the transition, you can use the ratio of the diameters given. Since the transition is described as a 30:1 transition, it means that the diameter at the top is 1/30th of the diameter at the bottom.
How does the ratio of the diameters give you the length of the transition?
Thia is a BT20 to BT50 transition:

And so is this:

Same ratio of diameters, different lengths.

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How does the ratio of the diameters give you the length of the transition?
The diameter ratio doesn't directly yield the transition length. Additional data, like transition shape or diameter change rate, is needed for its determination.

'Working on a transition for a build. To calculate the length of the transition, you can use the ratio of the diameters given.
The diameter ratio doesn't directly yield the transition length. Additional data, like transition shape or diameter change rate, is needed for its determination.

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