Thrust to weight ratio

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mpitfield

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How does one calculate the thrust to weight ratio. I have build that is roughly 1500 grams rounded up or 3.3 lbs and the motor I plan to use is is a CTI I255 thrust curve and specs found here
 
1500g = 1.5kg

255/1.5/10 = 17:1

the 10 is the g at sea level, 9.80665 m/s2 , I round up at 10

255/3.3/4.45 = 17:1
 
Last edited:
I get

(255 N) / (1.5 kg * 9.80665 m/s^2) = 17.3:1


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How does one calculate the thrust to weight ratio. I have build that is roughly 1500 grams rounded up or 3.3 lbs and the motor I plan to use is is a CTI I255 thrust curve and specs found here
Initial thrust on an I255 is roughly 60 lb on a rocket that weighs 3.3 lbs so 60/3.3=18.2:1. I like to use the thrust curve of the motor to see what the initial thrust spike is for my calculations. For the I255 the thrust spikes to approximately 60 lbs @ 0.056 sec. drops to 56 lbs @ approx. 0.11 sec then does a steady climb to the maximum thrust of 70.57 lbs @ approx. 0.34 when it starts a steady drop back to 56 lbs @ 1.7 sec to then drops to 0 at 2.04 sec. Using the average thrust of 56.87 lbs. gives you 17.23:1
Some times the initial thrust spike will kick a heavier rocket off the pad and get it to stable a flight speed even when the average thrust would say otherwise.
 
There are two "official" sources of hobby rocket motor performance data.

1.) The manufacture. https://www.pro38.com/motor/I255RL-16A.html

2.) The motor certification authority. https://www.canadianrocketry.org/mcc_motor.php?c=2&motor=517 I255-16A

All other may, or may not, be accurate depending on where and how the data was obtained and processed into motor files. If they are any questions, the way to resolve them is to go back to the original source of the data to check the motor files against the "official" sources.

The thrust to weight ratio is a valuable tool to make a zero order prediction of rocket performance. This is simply a non-dimensional ratio of two forces in consistent units: T, thrust (the propulsive force) divided by W, weight (the gravitational force).

The standard American engineering unit of force is the pound. If you know the motor thrust in pounds, and the rocket weight in pounds, simply divide the rocket thrust by the rocket weight to obtain the thrust to weight ratio. It's that simple.

In the rest of the world, and in the scientific community, the standard metric unit of force is N, the Newton. Force is the product of a mass multiplied by an acceleration or F = ma. "Weight" is the force (when measured in Newtons) that result as the product of a mass (when measured in kilograms) is multiplied by the acceleration of gravity (1gG = 9.80665 M/s^2 in MKS metric units). The nondimensional T/W ratio calculated from MKS metric units is T/W = T in Newtons divided by (weight in Newtons = mass in kg x 9.80665 M/s^2).

The T/W ratio is the same number whether you calculate it in American or metric unit because the units cancel out: T/W = T, N / W, N = T, lb. / W, lb.

The reason why the thrust to weight ratio is so useful, is that we can easily calculate the acceleration of any size rocket if we know the T/W ration when we non-dimensionalize the acceleration of gravity in units of g: a, g = T/W - 1. Once you know the acceleration of your rocket, you can estimate the maximum rocket velocity (not considering drag) if you know the burn time, or the minimum guidance length if you know the minimum air speed require for aerodynamic fin stabilization, in you head!

For example for the T/W = 6, the rocket accelerates upward at 6 - 1 = 5 g. Since 1 g ~= 9.81 meters per second every second in MKS or ~ 32.2 ft. per second every second in American engineering units, you can calculate the rocket gains 49.5 m/s of velocity every second in MKS velocity units, or 161 ft per second every second in American velocity units. If the motor burn time is 2 seconds, the maximum velocity would be 2 x a ~ 99 M/s = 322 fps ignoring drag loss.

It's really useful when someone claims their rocket broke mach and you know it's theoretically not possible even if there was no drag.......

Bob
 
There are two "official" sources of hobby rocket motor performance data.

1.) The manufacture. https://www.pro38.com/motor/I255RL-16A.html

2.) The motor certification authority. https://www.canadianrocketry.org/mcc_motor.php?c=2&motor=517 I255-16A

All other may, or may not, be accurate depending on where and how the data was obtained and processed into motor files. If they are any questions, the way to resolve them is to go back to the original source of the data to check the motor files against the "official" sources.

The thrust to weight ratio is a valuable tool to make a zero order prediction of rocket performance. This is simply a non-dimensional ratio of two forces in consistent units: T, thrust (the propulsive force) divided by W, weight (the gravitational force).

The standard American engineering unit of force is the pound. If you know the motor thrust in pounds, and the rocket weight in pounds, simply divide the rocket thrust by the rocket weight to obtain the thrust to weight ratio. It's that simple.

In the rest of the world, and in the scientific community, the standard metric unit of force is N, the Newton. Force is the product of a mass multiplied by an acceleration or F = ma. "Weight" is the force (when measured in Newtons) that result as the product of a mass (when measured in kilograms) is multiplied by the acceleration of gravity (1gG = 9.80665 M/s^2 in MKS metric units). The nondimensional T/W ratio calculated from MKS metric units is T/W = T in Newtons divided by (weight in Newtons = mass in kg x 9.80665 M/s^2).

The T/W ratio is the same number whether you calculate it in American or metric unit because the units cancel out: T/W = T, N / W, N = T, lb. / W, lb.

The reason why the thrust to weight ratio is so useful, is that we can easily calculate the acceleration of any size rocket if we know the T/W ration when we non-dimensionalize the acceleration of gravity in units of g: a, g = T/W - 1. Once you know the acceleration of your rocket, you can estimate the maximum rocket velocity (not considering drag) if you know the burn time, or the minimum guidance length if you know the minimum air speed require for aerodynamic fin stabilization, in you head!

For example for the T/W = 6, the rocket accelerates upward at 6 - 1 = 5 g. Since 1 g ~= 9.81 meters per second every second in MKS or ~ 32.2 ft. per second every second in American engineering units, you can calculate the rocket gains 49.5 m/s of velocity every second in MKS velocity units, or 161 ft per second every second in American velocity units. If the motor burn time is 2 seconds, the maximum velocity would be 2 x a ~ 99 M/s = 322 fps ignoring drag loss.

It's really useful when someone claims their rocket broke mach and you know it's theoretically not possible even if there was no drag.......

Bob

Hi Bob,

I really tried to focus on your answer this time and you had me right up to "In the rest of the world, and in the scientific community" in the 4th paragraph then things became cloudy until the last sentence.

I guess the saying "I'm no rocket scientist" applies...it's answers like this that remind me how limited I am intellectually.

All self-deprecating humour aside, I do appreciate your explanations and pick-up a bit more each time I read one.

Thanks
 
As Bob said, the thrust:weight ratio is the thrust divided by the weight. The common problem for 'mericans is that we measure weight in pounds, so to calculate the ratio you must convert Newtons (4.45N = 1lbf).

(255N / 4.45) / 3.3lb = 17x

However, since you listed your rocket weight in grams, just use Kilograms for the rocket weight (mass):

255N / 1.5Kg = 17x

That said, I don't like this rule of thumb much and prefer to use simulators to determine the rocket speed at the end of the launch guide, which is a much more useful value.
 
That said, I don't like this rule of thumb much and prefer to use simulators to determine the rocket speed at the end of the launch guide, which is a much more useful value.

Quite true--what may be rather on the slow side on a 4' rod may do just fine on a 6' or 8'. I don't know about OR, but Rocksim will tell you the height at which stable flight is achieved...

Later!

--Coop
 
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