Rear-eject pyramid simulation

[jmasterj]

I want to build a rear-ejecting pyramid rocket, but no one seems to make a kit for one anymore. No problem, they aren't terribly complicated to build from scratch. The challenge I am running through right now is how to simulate one in openrocket, particularly to try to determine how much nose weight to add. Attached is what I've come up with so far. Without the base drag cone, the CG and CP are in almost the same position.





I'm simulating with a cone, but will be building a pyramid. For scale, the base is 11" wide and that's a 29mm motor mount in a 3" mother tube inside. Motor is an F67W (should probably have picked a slower-burning one).

Any thoughts on how to simulate this better/more accurately? This sim (with the base drag cone) makes it look like there isn't any nose weight necessary, but the kit instructions I've been able to find all seem to have some.

 

[JoePfeiffer]

That's 'way outside the bounds of anything we can simulate.

 

[jmasterj]

That's 'way outside the bounds of anything we can simulate.

I should be able to calculate the CP of a pyramid kinda simply, right? Do you know where I could find that formula?

 

[PSLimo]

I've built plenty of paramids and I don't think you'd need a parachute. My 8" weighs 150 grams and my 16" weighs in at 1000 grams. Your 11" weight is in the middle and would flip over and decend slow enough without a chute.

If you take a look at this video of my 16" you'd also need a very short delay as they hit apogee pretty fast. At only a few hundred feet it might be back safe on the ground before the charge ejects.

 

[jmasterj]

I've built plenty of paramids and I don't think you'd need a parachute. My 8" weighs 150 grams and my 16" weighs in at 1000 grams. Your 11" weight is in the middle a would flip over and decend slow enough without a chute.

If you take a look at this video of my 16" you'd also need a very short delay as they hit apogee pretty fast. At only a few hundred feet it might be back safe on the ground before the charge ejects.

What materials did you construct them from?

 

[JoePfeiffer]

I should be able to calculate the CP of a pyramid kinda simply, right? Do you know where I could find that formula?

It ought to be simple, but I don't know where to look for someone who has done it. I'd start with Google (for once a "Google it" answer that isn't being rude! ), then see how Barrowman derived it for nose cones and see if I could come up with a similar approach.

 

[neil_w]

Applications like this are where I start to doubt the base drag CP hack. It is not intuitive to me that a little pyramid like this would have the CP so far back.

On the other hand, one might reasonably conclude (as I am doing in my head right now) that something like this would basically fly like a saucer, and it likely needs no nose weight at all. I mean, how much different is this from some of the Art Applewhite designs?

 

[mikec]

I mean, how much different is this from some of the Art Applewhite designs?

Most of those are flatter and have the motor farther forward, see https://www.artapplewhite.com/free.html

 

[PSLimo]

What materials did you construct them from?

I use foam board from a craft store for smaller saucers. Here's a pic of a 75mm prototype corresponding with Art Applewhite on the design 15 years ago that I used 2" pink foam insulation board.



On the larger 54 and 75mm I wet out a layer of light fiberglass over them. Here's a pic of the 54mm using hammered paint.


You might want to consider a larger 38mm motor mount, an 11" triangle is very draggy and your going to want to use shorter case motors. even a 1 grain G69 skid mark will put on a nice show.

 

[AlexBruccoleri]

As the person who designed and sold the first flying Pyramid kits with a fully functional rear-ejection system, I am happy to try to help. I can send anyone copies of the old instructions as well. The Cp is 1/3 the length from the rear. I generally like to have the Cg 1/2 the length of the Pyramid. In a sim, you should add a narrow tube that sticks out from the top centering ring toward to tip of the Pyramid. Let that be your nose weight and adjust its mass.

 

[Daddyisabar]

Isn't there someone reproducing the old Sunward Pyramid kits 24mm and 29mm.

 

[jmasterj]

Isn't there someone reproducing the old Sunward Pyramid kits 24mm and 29mm.

Is there? I'd love to know who that is!

 

[Steve Shannon]

The Cp is 1/3 the length from the rear.

This! It’s simply the centroid.

 

[kuririn]

Is there? I'd love to know who that is!

BnB Rockets.
Only the 24mm pyramid for now.
Tumble recovery, no rear eject.
https://bnbrockets.com/oscommerce/83

 

[kuririn]

Wouldn't be hard to modify it for rear eject.

 

[AlexBruccoleri]

This! It’s simply the centroid.

I am confused what you mean.

 

[AlexBruccoleri]

BnB Rockets.
Only the 24mm pyramid for now.
Tumble recovery, no rear eject.
https://bnbrockets.com/oscommerce/83

Those are a modification of the Sunward kits which were the copies of my kits. This looks a fair bit different, and I am confused why its just motor eject. Tumble recovery is a bit marginal on Pyramids, and if you can fly with a chute, you should. The key to my design was packing the chute between the centering rings and letting it fly apart in two pieces to avoid shock cord stress from a high speed ejection. On the 24 mm a streamer on the motor mount is fine or a small cute.

 

[Daddyisabar]

Is there? I'd love to know who that is!

He advertised on Facebook. Reproducing the Maverick. Bringing back Sunward kits.

 

[kuririn]

Here's the layout on the original Sunward Khufu's Pyramid kit.
Pop pod rear eject with streamer, main comes down on chute.



Alex, would have loved to purchase your pyramid kits but when I returned to the hobby they were already OOP.
BTW what's this about BMS selling your kits in the future (on your website)?

 

[Daddyisabar]

On King Tut the 29mm motor mount comes down fast on the streamer, not to everyone's taste. The Main body requires every bit of the thick plastic Sunward chute and needs the soft, fertile, Canadian soil to land (poke). A bit of a challenge to pack the first time but after ten flights it is no problem. Always a crowd pleaser because you really get to see and hear the usually over sized motors folks tend to use.

Pyramids are easy to scratch build. Big, high power ones with Metaphysical paint jobs rock.

 

[Steve Shannon]

I am confused what you mean.

The centroid (center of area) of a triangle is one third of up from the base.
Center of pressure on a simple geometric shape is located at the centroid of the shape.

 

[AlexBruccoleri]

The centroid (center of area) of a triangle is one third of up from the base.
Center of pressure on a simple geometric shape is located at the centroid of the shape.

It is interesting it works out that way. I was reviewing the equations in Barrowman's work and page 16 has the derivation for a cone. After reading it more, I was impressed with the depth of that work!

https://www.nar.org/wp-content/uploads/2016/01/barrowman_cp_extended_edition.pdf

 

[AlexBruccoleri]

Alex, would have loved to purchase your pyramid kits but when I returned to the hobby they were already OOP.
BTW what's this about BMS selling your kits in the future (on your website)?

Thanks! I only made one production run of the kits the Summer between high school and college. I should change the section on my website since BMS no longer sells them. Bill Saindon laser cut many of the parts for the original production run and I thought he might be interested in continuing them. I was not upset that Sunward copied the kits, I was upset they refused to acknowledge the designs and give a citation. I was doing a Ph.D. at MIT at the time and I had no time for hobby rocketry. Now that I am back into the hobby, I am happy to help a vendor make them or design better kits.

 

[3stoogesrocketry]

I should be able to calculate the CP of a pyramid kinda simply, right? Do you know where I could find that formula?

Cp is almost always 66 percent of the distance from the tip to the tail. That is how I always built mine including up to the 36 inch tall / wide models. Flew great on coffee can K motors. Rear eject out of 3 short 4 inch body tube each holding a 36 inch chute.

 

[AlexBruccoleri]

On King Tut the 29mm motor mount comes down fast on the streamer, not to everyone's taste. The Main body requires every bit of the thick plastic Sunward chute and needs the soft, fertile, Canadian soil to land (poke). A bit of a challenge to pack the first time but after ten flights it is no problem. Always a crowd pleaser because you really get to see and hear the usually over sized motors folks tend to use.

Pyramids are easy to scratch build. Big, high power ones with Metaphysical paint jobs rock.

I saw they used plastic..... My 29 mm kits used two thin mil nylon chutes from Top Flight Recovery. It added to the cost and likely reduced sales. I wanted the kits to be high quality and I did not regret using nice parachutes. The motor mount had a 9 inch chute.

I agree Pyramids are easy to scratch build. The shell on my K Pyramid is card board and it was fairly workable. That being said, a high quality kit is always nice. At least for me, the laser cut parts went together much better than my hand cut pieces did.

 

[jqavins]

If I'm not mistaken, and I feel pretty sure that I'm not, the CP is a matter of where lift operates, i.e. the reaction force from deflection of the path of air over a surface, which is not necessarily vertical. And base drag, though it creates a restoring force much like the lift provided by fins, is not caused by lift. So, base drag does not actually influence the true CP. It improves stability, an effect we approximate in simulations by adding that cone to move the simulated CP to where it needs to be for the same stabilizing influence.

So, if all that is right, the true CP would be a third of the way up, and base drag will make it as stable as if the CP were much further back. How should this be simulated? Well, just the way you've done it, with a real cone for the pyramid and the familiar weightless cone for the fake CP position. But, how large should it be?

Presented for your consideration:

Because most of the stabilizing force here will be from the base drag, and that drag depends directly on area, I propose using a cone diameter that gives the same base area as the pyramid you intend to build. For an 11" square base, that's 121 in², which means the cone's diameter should be 12.4 " in diameter.

 

[3stoogesrocketry]

If I'm not mistaken, and I feel pretty sure that I'm not, the CP is a matter of where lift operates, i.e. the reaction force from deflection of the path of air over a surface, which is not necessarily vertical. And base drag, though it creates a restoring force much like the lift provided by fins, is not caused by lift. So, base drag does not actually influence the true CP. It improves stability, an effect we approximate in simulations by adding that cone to move the simulated CP to where it needs to be for the same stabilizing influence.

So, if all that is right, the true CP would be a third of the way up, and base drag will make it as stable as if the CP were much further back. How should this be simulated? Well, just the way you've done it, with a real cone for the pyramid and the familiar weightless cone for the fake CP position. But, how large should it be?

Presented for your consideration:
View attachment 605706
Because most of the stabilizing force here will be from the base drag, and that drag depends directly on area, I propose using a cone diameter that gives the same base area as the pyramid you intend to build. For an 11" square base, that's 121 in², which means the cone's diameter should be 12.4 " in diameter.

You had a very long and elaborate way of backing up my saying of 66 percent down from the top lol.

 

[JoePfeiffer]

If I'm not mistaken, and I feel pretty sure that I'm not, the CP is a matter of where lift operates, i.e. the reaction force from deflection of the path of air over a surface, which is not necessarily vertical. And base drag, though it creates a restoring force much like the lift provided by fins, is not caused by lift. So, base drag does not actually influence the true CP. It improves stability, an effect we approximate in simulations by adding that cone to move the simulated CP to where it needs to be for the same stabilizing influence.

That's not the definition. From https://www.grc.nasa.gov/www/k-12/VirtualAero/BottleRocket/airplane/cp.html

"As an object moves through a fluid, the velocity of the fluid varies around the surface of the object. The variation of velocity produces a variation of pressure on the surface of the object as shown by the the thin red lines on the figure. Integrating the pressure times the surface area around the body determines the aerodynamic force on the object. We can consider this single force to act through the average location of the pressure on the surface of the object. We call the average location of the pressure variation the center of pressure in the same way that we call the average location of the weight of an object the center of gravity."

So it's the effect of the pressure on the whole object, which may or may not have anything to do with lift. The low pressure area aft of of the body (the base drag) is as valid a component of the CP as anything else.

 

[AlexBruccoleri]

If I'm not mistaken, and I feel pretty sure that I'm not, the CP is a matter of where lift operates, i.e. the reaction force from deflection of the path of air over a surface, which is not necessarily vertical. And base drag, though it creates a restoring force much like the lift provided by fins, is not caused by lift. So, base drag does not actually influence the true CP. It improves stability, an effect we approximate in simulations by adding that cone to move the simulated CP to where it needs to be for the same stabilizing influence.

So, if all that is right, the true CP would be a third of the way up, and base drag will make it as stable as if the CP were much further back. How should this be simulated? Well, just the way you've done it, with a real cone for the pyramid and the familiar weightless cone for the fake CP position. But, how large should it be?

Presented for your consideration:
View attachment 605706
Because most of the stabilizing force here will be from the base drag, and that drag depends directly on area, I propose using a cone diameter that gives the same base area as the pyramid you intend to build. For an 11" square base, that's 121 in², which means the cone's diameter should be 12.4 " in diameter.

The effect of base drag on the stability is non-trivial to calculate. You need a model of how the flow is separating around the edges. I recommend keeping the cg at 1/2 the length of the Pyramid. If it is further back, run some tests to confirm stability.

 

[Jeff Lassahn]

TL;DR: OpenRocket does this just fine. Use a cone with the same base area as the pyramid you want to build, and it will compute a CP that is 2/3 of the way back (like it did in one of your examples in the first post) which basically matches the practical advice of everyone who's been building these.

Now for some ranting.

THE BASE DRAG HACK DOESN'T WORK IN THIS CASE, JUST LIKE THE BASE DRAG HACK DOESN'T WORK IN A LOT OF CASES. We have no real reason to believe the base drag hack ever works right. As far as I can tell no one has ever done a careful comparison of a measured CP vs a CP calculated with the base drag hack. Ever. For any design at all.

Also, the CP is not the same as the center of area, or the centroid, or any other simple geometric calculation on a shape. For cones, it is close to the center of area. For fins it is not. For cylinders it is not. For saucer style shapes it's actually outside the object entirely (behind the back but usually not as far back as the base drag hack says). I think people get confused because the CG can be calculated by simple geometric arguments, so they assume the CP works the same way. It does not, the CP is a much more complicated beast than the CG and depends on lots of weird aerodynamic phenomena that are not easy to calculate. Anyone who gives you a "formula" for the CP is giving you a rough engineering approximation that works in some cases, not a result you can count on for everything.

OK, I'm done now.