# Rule of Thumb

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#### W.S.A.

##### Member
I am new to HPR (well starting out this weekend) and was wondering for the motor wise, is there a "rule of thumb" for the newton/weight ratio? Or it depends on what kind of effect you want the rocket to have? I have always use/heard that the max that the weight should be at 1/3 of total impluse. Is this correct?

I'd recommend you take the pad weight in pounds and multiply by 25 and make that your minimum liftoff Newtons of thrust....

5:1 Thrust to weight.
5:1 Newtons to pounds

5*5 = 25 --- as a minimum.

A typical T:W is more like 8 to 10.

So if your rocket weight 3 pounds on the pad, you need something like a 75-80 Newtons of thrust to get it going ... A G80 for instance....

YMMV -- this is a ROT....

Interesting enough..1/3 actually part of NAR Safety in that it states no weight limit but the rocket max weight should not exceed 1/3 of the impulse.

For rockets under 20 lb I been dividing avg impulse by 25 to determine maximum rocket weight.

ie G80: 80/25 yields rocket max weight ~ 3.2 Lbs

Last edited:
ie G80: 80/25 yields rocket max weight ~ 3.2 Lbs

For most motors, this conversion works well. However, several of the "long burn" motors (i.e. Loki I110, AT K185, many more) have a high initial thrust then taper off quickly leading to the "low" average thrust. When flying a long burn motor, it's best to look at the motor's performance graph (see thrustcurve.com) to better guage your max liftoff weight because the motor might actually be capable of lifting a heavier rocket than it's average thrust indicates. The key is what the motor's thrust is over the first 0.2-0.5 sec, after that the rocket should have cleared the rail and have enough speed for the fins to take over and stabilize it for flight.

For most motors, this conversion works well.

That's why it's a rule of thumb....works for most motors....there are exceptions.

These are from ROL's Info-Central, IIRC. Since the site is

Interesting enough..1/3 actually part of NAR Safety in that it states no weight limit but the rocket max weight should not exceed 1/3 of the impulse.

For rockets under 20 lb I been dividing avg impulse by 25 to determine maximum rocket weight.

ie G80: 80/25 yields rocket max weight ~ 3.2 Lbs
I think you're confusing total impulse with thrust. Thrust is the force or push of the motor in pounds or Newtons. Total Impulse is the integration of the thrust generated by a motor over the burn time and is expressed in either pound-seconds or Newton-seconds.

The average thrust over the first few tenths of a second while the rocket is guided by the launch rod is what is really important because the rocket needs to be moving at a velocity where the fins are providing aerodynamic directional control to your flight trajectory. Many studies have been conducted and for virtually all rocket using standard length launch rods, you want to have a 5:1 thrust to weight ratio to achieve a minimum 4G lift-off acceleration.

For smaller rockets with moderate sized fins you can be fairly certain that the fins are working at velocities over 20 mph (30 fps) and if you solve the equation d = v^2/(2a) where v is 30 fps, a = 4G = 4*32 fps2= 128 fps2 you will find that d = 3.5' is the minimum length of launch rod guidance length required for a rocket with a 5:1 T/w ratio so yo9u need at least a 4' launch rod to maintain this condition. Most model rocket kits actually have higher thrust to weight ratios.

Rockets with smaller fins will require higher rod velocities before aerodynamic control is obtained. Additionally in crosswinds exceeding 5 mph, you need more initial thrust to insure that your rocket velocity is even greater to that fins will not stall and loose control after your rocket has cleared the rod.

Ted Cochran authored this excellent report to provide guidance for the minimum thrust to weight ratios required to prevent stalls in higher cross winds https://www.nar.org/pdf/launchsafe.pdf however to summarize, you need the same T/W ratio as the wind speed in mph with a minimum of 5:1 at wind velocities to 5 mph and up to a minimim of 20:1 at the maximum allowable wind speed of 20 mph.

A conservative rule of this is the following.

1 pound of thrust = 4.45 newtons or ~5 newtons

A 5:1 T/w ratio means 5 pound of thrust is the minimum required for a 1 pound rocket which is exactly 22.5 newtons or approximately 5 x 5 = 25 N.

Dividing the average thrust of a motor by is easy to do in your head without a calculator. For example, the average thrust from a G80 is 80 N so divide this by 25 and you get 3.2 pounds as the approximate lift-off weight that gives a 4 G lift off acceleration. Using 80/22.5 you get 3.55 pounds, and if you look at the thrust curve and take the average thrust in the first 0.3 seconds the current production G80T motors https://www.nar.org/SandT/pdf/Aerotech/G80-20071207.pdf you find that the average initial thrust is 100 N so you can actually get a 100/22.5 4.4 rocket to lift off at 4 G if the motor lights promptly.

All this assumes that the wind velocity is at or below 5 mph. Since most folks don't measure wind speed directly, using the approximate method is good to ~7-8 mph in reality giving you a 2-3 mph margin on your wind speed estimation.

Bob

Thanks for that, I stand corrected on the mixing/reversing terms of impulse and avg. thrust.

For safest: check the thrust curve, etc especially in marginal situations.

Here's excerpt from NAR high power cert test pool which kind of relates to rule of thumb

"A10) What is the maximum allowable weight for a high power rocket permitted per NFPA
1127?
A) 100 pounds
B) 400 pounds
C) 3069 pounds
D) There is no limit provided the rocket weighs less than 1/3 of the average certified thrust of the
motors intended to be ignited at launch.
-----------------
The answer is "D". Refer to NFPA 1127, 2008 edition paragraph 4.9.1."

As a mechanical Engineer I use a number of NFPA and NFPA derived standards, they always have an excellent margin of safety.

Thanks for that report, it's now printed and cached in my rocketry bible binder

Thank you all for your awesome responses. I have looked and bookmarked all the resources that you gave me. I will keep you posted throughout my L1 cert experience.

Thanks for that, I stand corrected on the mixing/reversing terms of impulse and avg. thrust.

For safest: check the thrust curve, etc especially in marginal situations.

Here's excerpt from NAR high power cert test pool which kind of relates to rule of thumb

"A10) What is the maximum allowable weight for a high power rocket permitted per NFPA
1127?
A) 100 pounds
B) 400 pounds
C) 3069 pounds
D) There is no limit provided the rocket weighs less than 1/3 of the average certified thrust of the
motors intended to be ignited at launch.
-----------------
The answer is "D". Refer to NFPA 1127, 2008 edition paragraph 4.9.1."

As a mechanical Engineer I use a number of NFPA and NFPA derived standards, they always have an excellent margin of safety.

Thanks for that report, it's now printed and cached in my rocketry bible binder
You are correct that D is what is quoted in NFPA 1127-2008 4.9.1, however this question really should be removed from the test because the guidelines developed in Launch Safe have been adopted as the NAR flight safety recommendations and any experienced RSO will use the Launch Safe margins for flight safety decisions concerning the appropriate T/W ratios for a given launcher in windy conditions.

As the editor of the NAR S&T Motor Testing Handbook and as a professional in the aerospace field, I can state that without question there are errors, contradictions and omissions in NFPA 1122, 1125 and 1127, and that S&T is making a serious effort to correct and unify the 3 codes.

4.9.1 is an example of an error of omission in that it doesn't define the conditions where that T/W is acceptable. A rocket with a 3:1 T/W ratio accelerates at 2 G or 64 feet per second per second. While this level of acceleration may be acceptable for a guided rocket, an unguided rocket needs to obtain sufficient velocity under the guidance of a launch rod, rail or tower so that its fins achieve aerodynamic control of its ballistic trajectory before leaves the guidance device. If the day is dead calm with a 2 G acceleration you might be able to launch your rocket straight up without tip-off, but in the real world there is almost always wind, and high power rockets generally need to be moving at greater than 30 to 45 fps to insure free-flight aerodynamic stability. For a rocket with with a 3:1 T/W ratio the minimum guidance length to achieve 30 fps is 7' and 45 fps is 15.8 feet. With a 10 mph cross wind the required rod velocity doubles so you need 28' to 63' of guidance length, and in the maximum allowable 20 mph crosswind to avoid fin stall the rocket needs to reach 4 times that velocity or 120 fps to 180 fps to avoid fins stall induced tip-off. To do this you need a guidance length of between 112 to 250' which is unrealistic! Some folks would consider this length excessive but that's what the engineering data says is required for a rocket with a 3:1 T/W, and that's why 4.9.1 is misleading from from a safety standpoint.

MILITARY HANDBOOK MIL-HDBK-762(MI) DESIGN OF AERODYNAMICALLY STABILIZED FREE ROCKETS is the real deal for engineering derived requirements. You can download it free from several websites and its a valuable reference book if you really want to push the stability envelope.

Bob

Bob, gotcha.

What's your suggested Rule of thumb then?
Applicable in 'usual' situations and when a NAR S&T Motor Testing Handbook is not available at a launch. Like when someone is trying to determine if a vendor's on site motor available selection is sufficient?

John

The simplest rule of thumb is the take the average thrust and divide by 25 to get the maximum lift-off weight in pounds in winds at or below 5 mph

The problems associated with being this simple are 3:

1.) It does not take into account the delay. Heavier rockets may be on the ground before the ejection charge fires so you still need to sim the flight ahead of time.

2.) It is conservative. You might be able to safely loft a higher weight if there is an initial thrust spike for the first 0.3 to 0.5 seconds of the burn.

You can always look at the actual thrust curve and determine the average thrust for the first 0.3 to 0.5 seconds and use that as the thrust value that you divide by 25.

3.) It does not account for wind.

Accounting for higher wind velocities is easy. If the wind speed doubles to 10 mph, the the required T/W increases by a factor of 2, so the maximum safe weight is decreased by 2. At 15 mph, divide the weight by 3 and at the maximum allowable 20 mph wind speed divide the weight by 4. (This does not account for recovery wind drift, so you might want to reconsider whether you really want to launch at all and risk loosing your rocket.

This method works, however it really is what the RSO should be using if you don't have a sim for your flight. wRASP and other free simulators are available and are easy to use. If you know your rocket diameter and weight, assume a CD of 0.6 to 0.75 and have the thrust curve, the free simulators will do a reasonable job in simulating your flight profile within ~10% or so unless you have a very unusual rocket. You need to use the sim to determine you delay, so you might as well use it to figure out the lift-off acceleration of the rocket. Just remember to derate it for wind speed.

Bob

Also, keep in mind that 3:1 can be acceptable under certain limited conditions. I have seen a couple of spectacular launches in that range, done when there was zero ground wind and with a long (15 foot) rail. It also depends on the stability of the rocket. There isn't an exact answer, but 5:1 is a good general guideline in most cases (aside from windy conditions).

Also, keep in mind that 3:1 can be acceptable under certain limited conditions. I have seen a couple of spectacular launches in that range, done when there was zero ground wind and with a long (15 foot) rail. It also depends on the stability of the rocket. There isn't an exact answer, but 5:1 is a good general guideline in most cases (aside from windy conditions).
CJL

Absolutely correct and agrees with my math in the 10th post.

Every case is different. Rules of thumb are just that. They are conservative guidelines developed for those folks who do not have a sim program, or don't know how to evaluate a sim critically in borderline situations, or don't want to be bothered.

A correctly done sim is worth hundreds of rules of thumb, but folks need to learn to question a sim that doesn't make sense because it's probably using bad or incorrect data and therefore generating precisely inaccurate results.

Bob

What a wealth of information there is here on the forum. I had a question that I almost made a new thread on but, after a little searching there was no need to do it because just about anything you would ever need to know is already here somewhere.

I was trying to decide if I might be able to fly one of my rockets on one of the long burn motors and now I know!

Thanks to everyone who contributes here.

Yes I suspect that I could fly my 3 lbs rocket on an F240... but how high will it be at that point? So not all motors apply to this rule directly, but going below 5:1 particularly with wind is asking for it.

Yes I suspect that I could fly my 3 lbs rocket on an F240... but how high will it be at that point? So not all motors apply to this rule directly, but going below 5:1 particularly with wind is asking for it.
Use any sim to get 65'

T/W is fine, but unfortunately the shortest delay os 5 seconds so the rocket would be n the ground before the ejection charge fired. :shock:

Use any sim to get 65'

T/W is fine, but unfortunately the shortest delay os 5 seconds so the rocket would be n the ground before the ejection charge fired. :shock:

Short of drilling more of that delay out (and risking a cato) there is no way to fly it without electronics.

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