Weight: Speed vs. Altitude - The Sweet Spot

If you want a rocket to go as fast as possible, you need to make it as light as possible. Also, I've read in many places that more weight will decrease altitude. However, I've also read that a little added weight may decrease velocity during powered flight, but actually increase altitude, due to increased momentum. Playing around with OpenRocket, I've noticed that if I add a little nose weight, the altitude will sometimes increase up to a point, after which the rocket doesn't have enough oomph (that's the scientific term, I believe) to achieve its highest altitude.

So, my question is, if you're going for altitude over speed, how do you find the sweet spot of ideal weight (apart from playing around with it in a simulator)? Is there a mathematical formula for this (I assume there must be)? A rule of thumb? Does the motor matter? I mean, does the ratio differ depending on what motor you use?

Thanks!

https://www.rocketmime.com/rockets/studies.html

Bob

Daniel, I'm certainly no engineer and never played one on television but I think it's sort of like the question of why will a golf ball go faster and further than a ping pong ball when thrown by the same pitcher? I'm thinking wind resistance is more easily overcome by a more massive object? In the vacuum of space...hmmmm....never been there. I'm sure someone here can explain things better but I know from direct observation that it's hard to throw a feather.

tmacklin said:

Daniel, I'm certainly no engineer and never played one on television but I think it's sort of like the question of why will a golf ball go faster and further than a ping pong ball when thrown by the same pitcher? I'm thinking wind resistance is more easily overcome by a more massive object? In the vacuum of space...hmmmm....never been there. I'm sure someone here can explain things better but I know from direct observation that it's hard to throw a feather.

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Going the other direction, it is easier to throw a softball than a shotput.

Your right, you do need to find the sweet spot.

The term is 'Optimum Weight'. About the only way to find it is by running simulations, that's what they're for. Finding the most correct CD is incredibly important to altitude. First thing is ditching the lugs/buttons and using a tower launch. Second is as thin and streamlined a fin as you can go with. Believe it or not the finish plays an important part, a waxed rocket will go higher. On rockets not minimum diameter a boat tail will gain you altitude. A large amount of tracking smoke can play a part, too. There are artillery shells that will 'base bleed' smoke. This smoke fills in the space behind the rocket and lowers drag. Different nosecones affect altitude, especially when the rocket might be going through transonic regions. One factor that hasn't really been investigated is dimpling the cone to break up the boundary layer like a golf ball. A golf ball travels further with the dimples than ones without all other factors being the same. Drilling the dimples on a nosecone would be a study in patience if nothing else

This is an interesting discussion. On a personal note, I find getting the lead out of my ass to be a ongoing problem.

In answer to your other question the rocket weight needs to be optimized with the specific motor you plan on using. 👌

dave carver said:

The term is 'Optimum Weight'. About the only way to find it is by running simulations, that's what they're for. Finding the most correct CD is incredibly important to altitude. First thing is ditching the lugs/buttons and using a tower launch. Second is as thin and streamlined a fin as you can go with. Believe it or not the finish plays an important part, a waxed rocket will go higher. On rockets not minimum diameter a boat tail will gain you altitude. A large amount od tracking smoke can play a part, too. There are artillery shells that will 'base bleed' smoke. This smoke fills in the space behind the rocket and lowers drag. Different nosecones affect altitude, especially when the rocket might be going through transonic regions. One factor that hasn't really been investigated is dimpling the cone to break up the boundary layer like a golf ball. A golf ball travels further with the dimples than ones without all other factors being the same. Drilling the dimples on a nosecone would be a study in patience if nothing else

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Hmmm,.... I think I have my next build idea.

Happens I wrote a Sport Rocketry article on this subject back in January of 1998.

Optimal mass can be found by simulation, varying the mass until altitude is maximized. The optimal mass is dependent on drag coefficient. The lower the drag coefficient, the lower the optimal mass. (ASIDE: Optimal mass also depends on launch angle.) Of course, you rarely know drag coefficients, so for low and mid power rockets, I use the following method:

1) Select a credible range of drag coefficients

2) Compute optimal mass and altitude at each end of the range by ordered search with a simple altitude simulation routine. (The old routine, WRASP does this automatically)

3) Take the average of the two masses.

4) Compute the corresponding altitudes at both ends of the range.

In most cases, the altitudes for the average mass at the extremes are very close to the optimal altitudes at the same extremes. If not (which never happens for LPR and rarely happens for MPR), then it didn’t work.

** However, the main finding of the article is that it usually does work. **

That is, there usually is a relatively flat region near the maximum in the altitude/mass curve at a set (reasonable) drag coefficient.

Another approach to optimizing altitude is choosing a longer burning motor. One can overdo this to the point of detriment, just as one can overdo added mass. In fact, for low-impulse models (e.g.; and Estes Alpha on an A motor), the faster the burn, the higher the altitude. It turns out, though, that any time one can improve altitude by adding mass, one can improve it more by lengthening thrust time and decreasing thrust proportionately.

Should mention that (alas!) in most cases, the natural mass of the rocket is higher than the optimal mass.

I usually take Open Rocket, set the override on nose mass, arrange the windows so that I can see the apogee estimation, and slide the mass back and forth. Easy and seems effective. You will need real life testing to get the true optimum weight, but this estimate puts you in the ballpark. Obviously you will have to do some arithmetic to figure out the difference between starting mass and additional, but that is also easy.

dave carver said:

The term is 'Optimum Weight'. About the only way to find it is by running simulations, that's what they're for. Finding the most correct CD is incredibly important to altitude. First thing is ditching the lugs/buttons and using a tower launch. Second is as thin and streamlined a fin as you can go with. Believe it or not the finish plays an important part, a waxed rocket will go higher. On rockets not minimum diameter a boat tail will gain you altitude. A large amount of tracking smoke can play a part, too. There are artillery shells that will 'base bleed' smoke. This smoke fills in the space behind the rocket and lowers drag. Different nosecones affect altitude, especially when the rocket might be going through transonic regions. One factor that hasn't really been investigated is dimpling the cone to break up the boundary layer like a golf ball. A golf ball travels further with the dimples than ones without all other factors being the same. Drilling the dimples on a nosecone would be a study in patience if nothing else

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Drag reduction is definitely a complex science all on its own. We did some of that in the aircraft performance courses back in college. And, yes, surface finish makes a huge difference in skin friction. It also makes a big difference where that skin friction is, as believe it or not you can see an overall drag reduction by increasing surface friction in the right places. Weird, eh?

The golf ball analogy is off by a little bit though. The dimples help with reducing the turbulent flow area behind the MAC, and drawing the boundary layer in closer. There's a huge amount of base drag on a sphere and highly unstable flow. They do little or nothing ahead of the MAC. So from a rocket standpoint, you'd see little to no effect by dimpling a nose cone. But you may see some results from putting dimples on a boat tail.

From an aerodynamic standpoint, my educated guess is that most hobby rockets are very high drag. I've never actually bothered to calculate actual Cd's. Might be time for me to start doing some scratch building instead of just kits. Put some of that expensive education to use for once.

-Hans

HHaase said:

From an aerodynamic standpoint, my educated guess is that most hobby rockets are very high drag. I've never actually bothered to calculate actual Cd's. Might be time for me to start doing some scratch building instead of just kits. Put some of that expensive education to use for once.

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What would you consider a high C_D? Typical rockets are in the 0.5-1.5 range, with "perfect" ones in the 0.3 range. That seems high to me for such a simple shape (3FNC), but I don't have any training in this area.

I seem to recall, that long burn motors are the ones for those looking for speed and altitude, Vmax's and the like are really cool, but max velocity is achieved almost on the rail/or very close to the ground anyways. Long burns accelerate continously and combined with optimum weight give both altitude and speed, kind of like a high Ballistic Coefficient in a VLD rifle bullet, combined with a slower burning powder and a long barrel (less velocity lost over distance).

JohnCoker said:

What would you consider a high C_D? Typical rockets are in the 0.5-1.5 range, with "perfect" ones in the 0.3 range. That seems high to me for such a simple shape (3FNC), but I don't have any training in this area.

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Your numbers sound about right. And you're also correct that it is a high number for a simple shape with a small cross section. But there's a lot of factors that create drag.... and I'm very rusty, I haven't done a real calculation in about 15 years. I'd consider anything over 0.5 to be moderate drag, and over 0.8 to be high drag. That number would likely change quite a lot if I started testing and calculating actual rockets, as I said, it's a guess coming from a rusty education that's a bit out of date.

Rockets have a lot working against them from a drag standpoint. Lots of surface area, to create friction drag. High velocities, to create pressure drag. The base is a very sloppy area, due to the sharp base angle, which create a very turbulent flow that is a huge drag element. I'm not aware of many people, if any in the hobby realm, that actually calculate fin airfoil profiles for drag reduction. Launch lugs, and rail buttons, are big drag inducers. Very few designs look into area rule drag reduction. Competition guys take a lot of these into account. But for your average guy just out to have fun and make things go 'whooosh', it's not a huge deal. We have draggy rockets, it keeps them lower, which improves recovery and lets us see the flights better. And if we want to go higher, it's just more fun to run a bigger motor than spend a huge amount of time tweaking aerodynamics.

Most conventional model rockets are also dependent on high pressure levels. Think about how the Cg of an un-motored rocket is generally around the middle. Throw a motor in, and we're now tail heavy. So the Cp needs to be very far aft, necessitating larger fins. If the Cg was further forward, we could start doing longer aft tapers and smaller fins. But then we're talking a huge paradigm shift in model rocket design, and let's face it, the current state of model rocketry doesn't really require that dramatic of a change.

-Hans

just for grins I tried modding an Estes Alpha in open rocket. I changed the motor mount to a 13mm mount and the chute to a 12" x 1" streamer. gained 34m (154m Vs. 120m) A3-4t/A8-3, the delay was 0.15 seconds short .
Rex

Rex R said:

just for grins I tried modding an Estes Alpha in open rocket. I changed the motor mount to a 13mm mount and the chute to a 12" x 1" streamer. gained 34m (154m Vs. 120m) A3-4t/A8-3, the delay was 0.15 seconds short .
Rex

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In the Estes TR-11 they go into a upgraded Alpha. The best fin was an elliptical and the design changed to have a boat tail. The changes made a big difference. I have some mini A3-6's in my stash...hmmm...

bobkrech said:

https://www.rocketmime.com/rockets/studies.html

Bob

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This page was really informative. Actually, a lot of the responses were quite helpful.

Thank you!

rharshberger said:

I seem to recall, that long burn motors are the ones for those looking for speed and altitude, Vmax's and the like are really cool, but max velocity is achieved almost on the rail/or very close to the ground anyways. Long burns accelerate continously and combined with optimum weight give both altitude and speed, kind of like a high Ballistic Coefficient in a VLD rifle bullet, combined with a slower burning powder and a long barrel (less velocity lost over distance).

Click to expand...

Was taught the same.. speed adds to drag. Even with a long burn motor , rocket may really obtain a high velocity during its flight

Optimum size can be addressed before weight. Ie: get rid of payload section .

Kenny

KenRico said:

Was taught the same.. speed adds to drag. Even with a long burn motor , rocket may really obtain a high velocity during its flight

Optimum size can be addressed before weight. Ie: get rid of payload section .

Kenny

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Very true that as speed increases so does drag.

The whole 'momentum' argument is misleading.

Yes, a ping pong ball will slow down faster than a golf ball from velocity X but the input energy required to get it to that velocity in the first place is different and the argument is thus not applicable to our situation of comparing the same engine in the same rocket with different weights.

It is all about energy and energy losses.

In our case we are converting a set amount of chemical energy to kinetic energy (velocity) which is converted to potential energy (altitude). A light rocket goes faster given the same force applied for the same time. Drag is proportional to velocity squared so the lighter rocket experiences greater energy loss from drag.

Potential energy is proportional to mass so a heavy rocket does not go as high.

The sweet spot is where you balance the altitude loss due to energy loss from increased drag on a lighter rocket against the altitude loss from increased mass on a heavier rocket.

The short prescription for maximum altitude at a given impulse is more intuitive. It turns out that any time you are at or below optimal launch mass, you can get more altitude by lengthening the thrust time. (More generally, by adjusting the thrust/time curve.)

Therefore:
Make the rocket as light as possible, and then maximize altitude by varying the thrust profile. If you do the math, you will discover that the resulting configuration is above its optimal mass, but since you cannot lower the mass any further, that's optimal, and optimal mass isn't... (Because it isn't feasible)

One more thought on dimples affecting flight - remember that a golf ball has a large amount of spin (roughly 3000 rpm backspin for a driver, iron shots will be higher) that also interact with the boundary layer/dimples. I don't think you want to try to impart that to a rocket.

HHaase said:

Drag reduction is definitely a complex science all on its own. We did some of that in the aircraft performance courses back in college. And, yes, surface finish makes a huge difference in skin friction. It also makes a big difference where that skin friction is, as believe it or not you can see an overall drag reduction by increasing surface friction in the right places. Weird, eh?

The golf ball analogy is off by a little bit though. The dimples help with reducing the turbulent flow area behind the MAC, and drawing the boundary layer in closer. There's a huge amount of base drag on a sphere and highly unstable flow. They do little or nothing ahead of the MAC. So from a rocket standpoint, you'd see little to no effect by dimpling a nose cone. But you may see some results from putting dimples on a boat tail.

From an aerodynamic standpoint, my educated guess is that most hobby rockets are very high drag. I've never actually bothered to calculate actual Cd's. Might be time for me to start doing some scratch building instead of just kits. Put some of that expensive education to use for once.

-Hans

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Yeah, turbulent flow increases friction drag and decreases base drag. In bluff bodies (like a golf ball), where base drag far exceeds friction drag, dimples (which promote turbulent flow) are advantageous. In fine bodies (like a rocket), where friction drag far exceeds base drag, dimples are counter-productive.

Also, if a boat tail is doing its job, you don't need dimples. The idea of tripping the boundary layer at the rear end to reduce base drag is still a good one. That's what spoilers on race cars do.

More here:
https://sargrocket.org/documents/estes/tr-11.pdf

Larry Curcio said:

Yeah, turbulent flow increases friction drag and decreases base drag. In bluff bodies (like a golf ball), where base drag far exceeds friction drag, dimples (which promote turbulent flow) are advantageous. In fine bodies (like a rocket), where friction drag far exceeds base drag, dimples are counter-productive.

Also, if a boat tail is doing its job, you don't need dimples. The idea of tripping the boundary layer at the rear end to reduce base drag is still a good one. That's what spoilers on race cars do.

More here:
https://sargrocket.org/documents/estes/tr-11.pdf

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Ooh, that's a great document! Thanks!

I've downloaded a lot of great older and newer tech reports and other rocket docs in the last year, but this one is new to me.

You obviously missed the great "definitive Alpha fin shape" thread. Good for you.

JohnCoker said:

What would you consider a high C_D? Typical rockets are in the 0.5-1.5 range, with "perfect" ones in the 0.3 range. That seems high to me for such a simple shape (3FNC), but I don't have any training in this area.

Click to expand...

A lot of the time a drag coefficient is based only on frontal area of the airframe, for example when using RASP they only ask the diameter. If you calculate the full frontal area including fins, then you can use the lower Cd's for simple shapes, or use similar Cd's for rockets with different fins sizes, numbers and thicknesses. Surface area also plays a part, longer rockets will also have higher drag than simple shapes, and therefore scaling up an entire rocket should increase drag a bit compared to the frontal area. But otherwise, you can scale a rocket without changing Cd and that doesn't matter whether or not you're using the whole area or just the airframe, as long as you're consistent. OTOH, when considering rockets with unusually large or complex fins, calculating full frontal area, or a full simulation, is a must.

Larry Curcio said:

Therefore:
Make the rocket as light as possible, and then maximize altitude by varying the thrust profile. If you do the math, you will discover that the resulting configuration is above its optimal mass, but since you cannot lower the mass any further, that's optimal, and optimal mass isn't... (Because it isn't feasible)

Click to expand...

The problem with this approach is that there are a limited number of motors (for non research folk) or propellant and core shapes/sizes (for research folk) with which to work. The best motor might not be the lowest thrust because the lower thrust comes with lower ISP (mellow yellow is a good example). So in many cases you end up adding weight for the optimal altitude.

Zebedee said:

The problem with this approach is that there are a limited number of motors (for non research folk) or propellant and core shapes/sizes (for research folk) with which to work. The best motor might not be the lowest thrust because the lower thrust comes with lower ISP (mellow yellow is a good example). So in many cases you end up adding weight for the optimal altitude.

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Yes! I absolutely agree.

Was just trying to show a broader context than optimal mass, which I thought made more intuitive sense than optimal mass by itself.


Regards,
-Larry