MACH DIAMONDS and exhaust gases/ mid power

Back in the late 1990's or there abouts a section appeared in HPR magazine about a flyers method to build a mach buster. It was a 29mm diameter rocket on a G40w. I began thinking about that as I have seen a few articles on mach diamonds and how you cant hit mach speed unless the exhaust exits at mach speed.(visual conformation as with diamonds) So can a min. diam. 29mm rocket really hit MACH and beyond on a mid-power G ?
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yes the Apogee Aspire is a perfect example. small light weight rocket that can hit mach with a G80.

I think you can do it on a F-motor. Just have to build it light and strong.

Estesbasher said:

I think you can do it on a F-motor. Just have to build it light and strong.

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I'm sure you probably can if you build light enough!

This rocket here I just stared. I wanted to see just how fast I could get one to go on a G-80. Right now where it sits it's at 3oz. I'm trying to keep it under 10oz. ready to fly.
I've just got to run it through rock simms. To see if I want to build it with 3-fins or 4. But I want to see just how close I can come to a 1000-mph on the G-80-14

crazyed said:

Back in the late 1990's or there abouts a section appeared in HPR magazine about a flyers method to build a mach buster. It was a 29mm diameter rocket on a G40w. I began thinking about that as I have seen a few articles on mach diamonds and how you cant hit mach speed unless the exhaust exits at mach speed.(visual conformation as with diamonds) So can a min. diam. 29mm rocket really hit MACH and beyond on a mid-power G ?
View attachment 187766

Click to expand...

A few comments on the premise for the question:

Both composite and BP motors have supersonic exhaust streams. A typical Isp for BP, for example, is 80 lb*sec/lb. That corresponds to an effective exhaust velocity of about 2600 ft/sec – supersonic. You would likely see Mach diamonds in the exhaust, except that it’s full of smoke and charcoal particles. Composite motor exhaust streams are two or three times as fast. You can probably see MD’s in the exhausts of Blue Thunder motors, which are relatively clear.

Also, in principle, you don’t require a supersonic exhaust stream to have a supersonic rocket. Think about it. If you can have an exhaust stream that travels faster than the rocket, why can’t you have a rocket that travels faster than the exhaust? In free space, the DeltaV supplied by a rocket motor is given by the Rocket Equation:

DeltaV=EffectivExhaustVelocity*Ln(LaunchMass/BurnoutMass)

The argument of the natural logarithm (Ln) is called the Mass Ratio. In free space, you need a mass ratio of about 2.7183 for a rocket to reach the speed of its exhaust gasses. At higher mass ratios, rockets in free space can exceed the speeds of their exhausts.

Rockets on earth can exceed the speeds of their exhausts, but mass ratios must be higher, and there are also thrust-to-weight ratio requirements – all because of gravity and drag. Those are huge requirements for a model rocket – but they are unnecessary to break Mach 1, given the propellants we use.

Not sure if any of that was productive, but there it is...

Best Regards,
-LarryC

This is a pic of my scratch build on a G-185 V-MAX you might not see the mach diamonds but on the field you could if you didn't blink!!

Primativerocketry said:

View attachment 187805
This is a pic of my scratch build on a G-185 V-MAX you might not see the mach diamonds but on the field you could if you didn't blink!!

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They are very hard to see on this picture...

Blues (G80T)



Greens (G76G, G78G)


I've seen them in reds but it's hard to catch. White is just all fire and smoke.

A few comments on the premise for the question:

Both composite and BP motors have supersonic exhaust streams. A typical Isp for BP, for example, is 80 lb*sec/lb. That corresponds to an effective exhaust velocity of about 2600 ft/sec – supersonic. You would likely see Mach diamonds in the exhaust, except that it’s full of smoke and charcoal particles. Composite motor exhaust streams are two or three times as fast. You can probably see MD’s in the exhausts of Blue Thunder motors, which are relatively clear.

Also, in principle, you don’t require a supersonic exhaust stream to have a supersonic rocket. Think about it. If you can have an exhaust stream that travels faster than the rocket, why can’t you have a rocket that travels faster than the exhaust? In free space, the DeltaV supplied by a rocket motor is given by the Rocket Equation:

DeltaV=EffectivExhaustVelocity*Ln(LaunchMass/BurnoutMass)

The argument of the natural logarithm (Ln) is called the Mass Ratio. In free space, you need a mass ratio of about 2.7183 for a rocket to reach the speed of its exhaust gasses. At higher mass ratios, rockets in free space can exceed the speeds of their exhausts.

Rockets on earth can exceed the speeds of their exhausts, but mass ratios must be higher, and there are also thrust-to-weight ratio requirements – all because of gravity and drag. Those are huge requirements for a model rocket – but they are unnecessary to break Mach 1, given the propellants we use.

Not sure if any of that was productive, but there it is...

Best Regards,
-LarryC

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Well put, Larry. In theory one does not need Mach diamonds to go faster than the speed of sound, but the higher the exhaust velocity, the faster the rocket will go.

Great information from all and thankyou.. I thought it was possible on the G80 but BP was a pleasant surprise. So MACH diamonds would likely be present if not for the smoke on some BP motors.Nice..
More projects

Estesbasher said:

This rocket here I just stared. I wanted to see just how fast I could get one to go on a G-80. Right now where it sits it's at 3oz. I'm trying to keep it under 10oz. ready to fly.
I've just got to run it through rock simms. To see if I want to build it with 3-fins or 4. But I want to see just how close I can come to a 1000-mph on the G-80-14

Click to expand...

Thats pretty cool... Keep us informed

crazyed said:

Back in the late 1990's or there abouts a section appeared in HPR magazine about a flyers method to build a mach buster. It was a 29mm diameter rocket on a G40w. I began thinking about that as I have seen a few articles on mach diamonds and how you cant hit mach speed unless the exhaust exits at mach speed.(visual conformation as with diamonds) So can a min. diam. 29mm rocket really hit MACH and beyond on a mid-power G ?
View attachment 187766

Click to expand...

If your exhaust isn't supersonic, you're not going to be producing much thrust. Thrust is equal to mass flow rate times exhaust velocity. Since there isn't a lot of mass flow, most of the thrust comes from accelerating the exhaust to high speeds. This is achieved by using the nozzle at the back of every rocket motor you see. The particular type of nozzle is called a converging-diverging (CD) nozzle. The exhaust is accelerated to Mach 1 at the throat, and further expansion will generally accelerate the flow even more to supersonic speeds. The maximum Mach number of the exhaust is governed by the expansion of the nozzle, which is a function of the atmospheric pressure and the chamber pressure.

For more information, read up on converging-diverging (de Laval) nozzles.

DizWolf said:

Blues (G80T)

Greens (G76G, G78G)

I've seen them in reds but it's hard to catch. White is just all fire and smoke.

Click to expand...

Thanks for the great "example pics of Mach Diamonds"

The flames pm the super thunder propellant look much more impressive then the standard blue thunder. If the vendor at the upcoming GHS launch has them I want to try an H550 ST at the night launch.

Here's a few. The G-76
You don't get much on the white lighting. But I like how they look.

As was previously stated, the exhaust velocity of all hobby rocket motors with convergent/divergent nozzles will be supersonic. Whether you can see the mach diamonds depends on the opacity of the exhaust plume.

Whether your rocket can exceed the speed of sound depends on number of factor: the rocket weight and diameter, and the thrust of the motor and the total impulse.

Without doing all the math and leaving out drag, the acceleration in g of a rocket is determined by the thrust to weight ratio of the rocket: a(g) = (T/W) - 1 where g = 9.8 m/s/s, and the velocity of a rocket is determined by the burn time of the rocket motor: v = at and Mach 1 ~= 340 m/s

A 0.5 pound rocket weight 0.5 lb x 4.45 N/pound = 2.22 N. A rocket motor with a thrust of 80 N will have an initial acceleration of (80/2.22)-1 g = 35 g. v = 35 g x 9.8 m/s/s/g = 343 m/s/s so it would take about 1 second to reach Mach 1 if drag is not considered.

But drag counts. Drag is proportional to the effective cross-sectional area of the rocket, the atmospheric density and the velocity squared. The effective cross-sectional area is equal to the actual cross-sectional area c Cd (the drag coefficient). A minimum diameter rocket for a 29 mm motor has a drag of 56.1 N with a Cd = 1, and will never reach Mach 1 unless the Cd is much lower. For the hypothetical 29mm MD 0.5 pound lift-off weight rocket to reach or exceed Mach 1 with an AT G80T, the Cd must be <= 0.67.

It is very difficult to make a 29 mm rocket that weighs less than 4 oz. without a motor, but that about what it will take to break Mach 1 with an AT G80T. The Apogee Aspire has a listed weight of 1.85 oz. (no paint) so it stands a chance if built light.

A generic sim for this example was done in RASAero. I would sim your rocket design first to make sure it will be close. Without electronics it is difficult if not if not impossible to verify your flight.

Bob

So like you said it's not impossible with the right rocket.

Going to try and get a pic of those Mean Green Mach Diamonds next Sat. 2 G76-10G in my LOC 4-29SS. Nowhere near Mach But should be nice.
A continued thanks for all of the knowledge being shared here.

Tight aperture, fast shutter. Photo will be a little dark. But if you're too wide or too slow, you'll just get a pretty green flame

Sorry.. no pics.too dog-gone fast on those G-76 motors.

crazyed said:

Thats pretty cool... Keep us informed

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I flew this rocket yesterday on the G-80-14 for a altitude of 6116'
Here is a picture of a 29mm rocket I flew on the same motor. I never got the altitude on it because I had a problem with the altimeter.

Awesome job and great pic. SARA has a launch Sunday (NOV.16). I hope to get a pic or 2 of flights catching the illusive Mach Diamonds.There have been alot of great shots posted here and hope to see plenty more.

Here's a couple of "Screen Captures" (Pics' I took of my Screen while pausing the Video I took) from my recent Flight of my TLP Martel on an E-20.






No Diamonds, but plenty of Firey Gasses!