# How much will it lift?

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#### gary7

##### Well-Known Member
TRF Supporter
I have been trying to find an article or something with formulas for determining the lift capability of rocket engines. In other words, how much will engine "x" lift in terms of weight? Any related information such as predicting velocity and rocket altitude would also be appreciated. I have only a very basic understanding of engine nomenclature but never really understood or learned all the details re impulse, thrust, newtons, etc. Anyone who can direct me to an easy to understand explanation of this info would also be very much appreciated. Yes, I have searched many of the educational sites but I just don't get it. Certainly I am the only person with this problem. I can only get better and feel more comfortable with rocketry if I know these things. Thanks!

In general, you want a liftoff thrust that is 4-5 times the weight of your rocket, at an absolute minimum. In many high power rocket motors, the liftoff thrust is fairly close to the average thrust. In these cases, the motor can lift a rocket weighing roughly 1/5 of the average thrust. Since the average thrust is in Newtons, and there are 4.45 newtons per pound, this means that a rocket motor can lift 1 pound for every 22 newtons of thrust. Therefore, a G80 can lift around 3.5 pounds.

In some cases, the initial thrust is significantly higher than the average thrust though, and the initial thrust is what matters for the ability to safely lift off. For example the Aerotech K185 has an average thrust of 185 newtons. From the relationship described above, you would expect it to be able to lift roughly 185/22 = 8.4 pounds. However, if you look at the thrust curve of the K185 (https://www.thrustcurve.org/simfilesearch.jsp?id=962), you will notice that over the first 2 seconds, the motor is putting out roughly 320 newtons of thrust. Because of this, it could actually lift a 13-14 pound rocket safely, although I probably wouldn't recommend it except on the calmest of days (when you push the weight limit on a long burn motor, it tends to arc over a long ways).

This is my basic understanding regarding motors in our hobby.

The first letter is an indication of the energy bracket the motor falls into; it represents the total amount of energy the motor contains. A "B" has about twice the energy of an "A" motor, and a "C" motor has about twice the energy of a "B" motor. This is at the upper end of the energy bracket.

The numeric value is the average rate at which the energy is released over time. A higher number means a higher release rate of energy. A number of "12" is releasing its energy about twice as fast as a "6", resulting in twice as much thrust or "push". This "push" can be measured in the Customary Units of pounds or the metric units of newtons.

I am sure others can give a more precise definition, but this should get you going.

Greg

Like cjl says, you can see some of this with the thrustcurve for a J350.

You can see that the average thrust is a bit lower than the initial thrust, which, all things being equal, is a better situation to ensure stable flight off of the rod/rail/tower/tube. With the 5-to-1 rule in this case, the average thrust in pounds is 83.8, so you could launch a rocket up to 16.8 pounds (83.8 / 5). However, theoretically, you could launch something that almost weighed 27 pounds with this motor, and still be at the 5-to-1 rule, because of the initial kick within the first moments that the motor is burning. Anything that weighs less makes the rocket go faster/higher.

Greg

So would the thrust of engine clusters be cummulative? In other words, would the thrust or power of a cluster of two or three engines be enough to lift a rocket with twice or three times the weight that a single motor could lift?

Yes. The thrust of each motor is summed to get the total thrust.

You may recall that the first stage of the Saturn V moon rocket (S-IC) had 5 x F-1 rocket engines. Each engine had a sea level thrust of about 1.5 million pounds of thrust. The cumulative effect of all engines at rated pressure was 7.5 million pounds of thrust.

Greg

So would the thrust of engine clusters be cummulative? In other words, would the thrust or power of a cluster of two or three engines be enough to lift a rocket with twice or three times the weight that a single motor could lift?

Yes.

Like cjl says, you can see some of this with the thrustcurve for a J350.

You can see that the average thrust is a bit lower than the initial thrust, which, all things being equal, is a better situation to ensure stable flight off of the rod/rail/tower/tube. With the 5-to-1 rule in this case, the average thrust in pounds is 83.8, so you could launch a rocket up to 16.8 pounds (83.8 / 5). However, theoretically, you could launch something that almost weighed 27 pounds with this motor, and still be at the 5-to-1 rule, because of the initial kick within the first moments that the motor is burning. Anything that weighs less makes the rocket go faster/higher.

Greg

You also want to keep in mind whether the rocket will get high enough for a safe deployment. A J350 can safely lift 25lbs, but it will only get to around 500 feet if you do so. That might cause a problem for deployment, and you would have to plan accordingly.

I thought the rule was 6-1 ratio for safe flite

I thought the rule was 6-1 ratio for safe flite

I've heard a variety of "rules of thumb". The truth is, there are a lot of things to keep in mind. A stable, proven rocket with a decent length rail on a calm day can pull of 3:1 or 4:1 without difficulty. Most rockets can do 5:1 or 6:1 on an average length rail on a calm day, and fly beautifully. Other rockets are more questionable (see below for more detail than you ever needed to know), and need a harder kick to be stable. On a breezy day, go at least 10:1, with more like 15:1 if the winds are higher (but still within safe limits).

The speed a rocket needs for stability is variable, but as a general rule, it depends on three things. First is the distance between the center of pressure and the center of gravity. The smaller this is, the faster a rocket will need to be going to be stable. Second, it depends on the force the fins will develop when at a given angle of attack. For the most part, you can approximate this by scaling it with the area of the fins. Highly swept fins will be slightly less efficient at this, and low sweep will be more efficient, but that's a smaller effect. Finally, it depends on the moment of inertia of the rocket in the axis perpendicular to the tube. If you have a ton of noseweight and a heavy motor, the moment of inertia will be higher. Also, if the rocket is longer, the moment of inertia will be higher. This means that it will take a greater restoring moment to cause the same effect, and it will (effectively) slow the ability of the rocket to correct itself. If your rocket is stubby, lightweight rocket with 2 calibers of stability and huge fins, it will need much less speed for stability than a long rocket with a ton of noseweight, small fins, and a static margin of 1. My AIM-120C AMRAAM is a good example of a rocket that needs a very high speed for stability. It has 10 pounds of noseweight and uses large, heavy motors, and it only has about 1.5 calibers of stability. However, its fins are not very large, and include decent sized canards. Because of this, my AMRAAM requires a much, much higher velocity for stable flight than would a standard rocket. On the other end of the scale is something like a Big Bertha. It is lightweight, has huge fins, and a very large margin of stability. As a result, it will happily fly at very low airspeeds with perfect stability.

In addition, the entire paragraph above is dealing with the airspeed required for safe flight. Once you have figured out whether your rocket needs average, above average, or below average airspeed for flight, then you have several possible ways to obtain that airspeed. You get the same airspeed with a fast burning motor off a short rod as you would off a long rod with a slower burning motor. It's all a balance of the factors required for safe flight, and it isn't quite as simple as many people think.

This is why any "4:1" or "5:1" or "6:1" rule is just an estimate for an average rocket, and not always applicable. In general, I would go with at least 8 or 10 to 1 for an unproven design on a first flight, as the factors above could affect the way it flies significantly. Once it has proven stable, and if it doesn't appear to be excessively wobbly off the pad, you can go for the slow, majestic liftoffs.

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.... First is the distance between the center of pressure and the center of gravity. The smaller this is, the faster a rocket will need to be going to be stable.

I agree with what you say about different rockets needing different speeds to be stable coming off the rod/execpt, except the first one.

The further apart the CP and CG are, the more speed you need coming off the rod/rail. When the CP is further away, the sideways forces generated by the fins from the cross wind has a longer lever to the CG and will cause more weathercocking. Over stable rockets are much more prone to weathercocking then rockets with about 1 caliber of stability.

Other then the first point, the other two points you had are spot on!

I agree with what you say about different rockets needing different speeds to be stable coming off the rod/execpt, except the first one.

The further apart the CP and CG are, the more speed you need coming off the rod/rail. When the CP is further away, the sideways forces generated by the fins from the cross wind has a longer lever to the CG and will cause more weathercocking. Over stable rockets are much more prone to weathercocking then rockets with about 1 caliber of stability.

Other then the first point, the other two points you had are spot on!

Nope - a larger stability margin minimizes the speed needed for stable flight by increasing the restoring moment for a given angle of attack at a given airspeed. Any rocket that is stable at extremely low speeds will also be more susceptible to crosswinds as well, but that is a slightly different issue (and I would always recommend higher T:W ratios in windy conditions).

The dreaded weathercocking..... iv gotten a couple lawn darts because of this:y:

Nope - a larger stability margin minimizes the speed needed for stable flight by increasing the restoring moment for a given angle of attack at a given airspeed. Any rocket that is stable at extremely low speeds will also be more susceptible to crosswinds as well, but that is a slightly different issue (and I would always recommend higher T:W ratios in windy conditions).

You are correct. I do understand the fin/CG/CP relationship as you explained it. I was thinking in terms of a vertical flight instead of only a stable flight.

As a practial matter, assuming sufficient speed for a stable flight, you still need more speed comming off the rod/rail with over-stable rockets to counter the effects of crosswinds, because the fins are more effective with the larger distance between CG/CP, to insure a vertical flight.

You are correct. I do understand the fin/CG/CP relationship as you explained it. I was thinking in terms of a vertical flight instead of only a stable flight.

As a practial matter, assuming sufficient speed for a stable flight, you still need more speed comming off the rod/rail with over-stable rockets to counter the effects of crosswinds, because the fins are more effective with the larger distance between CG/CP, to insure a vertical flight.

All of the things I mentioned above as requiring a higher speed for stability also make the rocket less prone to weathercocking (because of the reduced ability of the fins to correct at low speeds). In addition, if your rocket is slow off the pad, there's a higher effective angle of attack that it is initially flying at, so not only is it more effective at correcting, it has a larger angle to "correct" for with the same windspeed. So, if you have a lightweight rocket with big fins and a large stability margin (like a Big Bertha), expect much more weathercocking than with a heavy, small-finned rocket with a questionable stability margin (like my AMRAAM).

Here's a simple chart I've put together for my NARCON 2010 presentation on the atmosphere and how it effects rocket flight.

It shows the minimum recommended launch rod guidance length for a given wind velocity range and thrust to weight ratio of a rocket/motor combination.

It is an outgrowth of Ted Cochran's Launch Safe Report analysis on what is required to have a straight, non-weathercocking flight https://www.nar.org/pdf/launchsafe.pdf

Bob

View attachment launch wind speed.pdf

A simulation program like Open Rocket (free) or Rocksim (not free except trial)
Or even Thrustcurve.org (free)
will approximate the speed off the rod/rail in order to have enough speed so the fins can work as it leaves the support. Also this will give you thrust to weight ratios as well as altitude expected and approx delay times. Thrustcurve is fairly conservative and want to see 50fps.
Most rockets can be successfully flown at 40fps off the rod/rail if its a low wind day. Using simulation programs, I haven't had an issue.

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