Thrust:Weight Ratio -- Why 5:1?

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MetricRocketeer

MetricRocketeer

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Hi everyone,

A safe thrust:weight ratio is 5:1 or higher. That is the rule of thumb.

But why that ratio? I am not disputing its accuracy, but what is the explanation for those values?

Thank you.

Stanley
 
It is based on the acceleration needed to develop a safe velocity off standard guides. You want the rocket aerodynamically stable before leaving the mechanical guide.

5:1 thrust to weight should give an adequate margin of safety for any but the shortest rods.
 
I think the NAR sanctioned launch minimum is 3:1. But, as mentioned, it’s a rule that has lots of assumptions. A better guideline is a speed off the rail/rod of 4x the crosswind speed. Why? Because an average fin stalls at an angle of attack of 15 degrees. The sine of 15 is .25. The inverse of that is 4.

There’s still an assumption in that, but its narrower.

I’ve heard that humans are not good at detecting wind speeds under 5 mph without tools. So that sets a practical minimum. If it seems dead calm, it could still be 5 mph. If launch rods are 2.5” usable length, then s = 1/2at^2. 2.5=1/2 x 32x3 t^2. T^2 = 5/96. T = 0.23sec. V=at. V=96x0.23. V= 22 fps. Or 15 mph. Good to a cross wind of just under 4mph.
 
Charles_McG said:
I think the NAR sanctioned launch minimum is 3:1. But, as mentioned, it’s a rule that has lots of assumptions. A better guideline is a speed off the rail/rod of 4x the crosswind speed. Why? Because an average fin stalls at an angle of attack of 15 degrees. The sine of 15 is .25. The inverse of that is 4.

There’s still an assumption in that, but its narrower.

I’ve heard that humans are not good at detecting wind speeds under 5 mph without tools. So that sets a practical minimum. If it seems dead calm, it could still be 5 mph. If launch rods are 2.5” usable length, then s = 1/2at^2. 2.5=1/2 x 32x3 t^2. T^2 = 5/96. T = 0.23sec. V=at. V=96x0.23. V= 22 fps. Or 15 mph. Good to a cross wind of just under 4mph.
Click to expand...
Hi Charles,

Thank you very much for your reply.

I would very much like to follow your argument. But could you please restate it line by line, and explain your variables. That way I could understand it better.

Stanley
 
MetricRocketeer said:
Hi Charles,

Thank you very much for your reply.

I would very much like to follow your argument. But could you please restate it line by line, and explain your variables. That way I could understand it better.

Stanley
Click to expand...

I will, Stanley. Tonight or tomorrow - it’s a family day today.
 
MetricRocketeer said:
Hi Steve,

So ultimately, Thrust * Gravity / Weight = Acceleration.

If you would, please, how does this tell us that Thrust / Weight = 5?

Thank you.

Stanley
Click to expand...

It’s just a rule of thumb that saves RSOs from requiring that every flyer justify their motor choice by providing a simulation.
For typical rail lengths 5:1 results in a velocity of somewhere around 45 — 50 FPS when the rocket leaves the rail, which is generally accepted as the minimum needed for stability. For a longer rail 4:1 or even 3:1 can work.
NFPA 1127 actually requires 3:1 average, but because most motors have a thrust spike just after ignition, that typically works out as 5:1 initially.
With the equations I provided and the standard motion equations (v=a*t and d=v*t) you should be able to calculate the velocity for every thrust to weight ratio given an 8 foot rail. Or the length of rail needed to achieve 45 FPS given a particular T:W.
 
Charles_McG said:
I think the NAR sanctioned launch minimum is 3:1. But, as mentioned, it’s a rule that has lots of assumptions. A better guideline is a speed off the rail/rod of 4x the crosswind speed. Why? Because an average fin stalls at an angle of attack of 15 degrees. The sine of 15 is .25. The inverse of that is 4.

There’s still an assumption in that, but its narrower.

I’ve heard that humans are not good at detecting wind speeds under 5 mph without tools. So that sets a practical minimum. If it seems dead calm, it could still be 5 mph. If launch rods are 2.5” usable length, then s = 1/2at^2. 2.5=1/2 x 32x3 t^2. T^2 = 5/96. T = 0.23sec. V=at. V=96x0.23. V= 22 fps. Or 15 mph. Good to a cross wind of just under 4mph.
Click to expand...

2.5 inches?!

There might be something to that 3:1 ratio, for MR at NAR sanctioned launches, but that presumes that conditions are ideal and that the launcher is of sufficient length. HPR should have higher margins for safety, due to the higher energies (injury or damage potential) involved. So 5:1 is reasonable for HPR, and if you have to ask the question, maybe you should not be testing the limits. The limits generally applied at sanctioned events is the Manufacturers Maximum Recommended Gross lift off Mass, but even that is not absolute, and T/W is a good discussion point.

Alan
 
Charles_McG said:
I think the NAR sanctioned launch minimum is 3:1...
then s = 1/2at^2....
2.5=1/2 x 32x3 t^2.
Click to expand...
Good point about the relative wind speed, that is very important. This is a good illustration and shows how the motion is related to acceleration via the thrust force, but it looks like you are using an acceleration-to-gravity ratio there, a:g=3:1, rather than a Thrust/Weight ratio. The two are related by (a/g) = ((T/W) - 1).

Thrust - Weight = mass*acceleration (ignoring the aerodynamic Drag force which is still small when V is near zero)

W*((T/W) - 1) = ma
mg((T/W) - 1) = ma

((T/W) -1) = (ma)/(mg)

(T/W - 1) = (a/g)

so, if you wanted to use a T/W ratio of 3:1, then you would get an acceleration of (3-1) or 2g. Consider the special case of Thrust=Weight, you would have T/W = 1 and zero acceleration.

another reference for the equations of motion, assuming constant acceleration, average velocity, kind of shows how the Force equation is related to the Motion equation through the acceleration.

https://www.physicsclassroom.com/class/1DKin/Lesson-6/Kinematic-Equations
 
Yeah, I noticed the acceleration vs T:W ratio being off by one. I used those numbers (other than the inch instead of foot typo) because I knew that it makes a nice story relating the NPFA 3:1 minimum, the 15 degree maximum angle of attack, typical LPR rod length, and the maximum wind speed most people would say is ‘calm’. Great story - not perfect in the details.

As Steve points out, it’s a rule of thumb - not the complete story. Stanley is looking for the ‘how do you arrive at that particular number’ back story. My reasoning get you close. Maybe close enough to round. When I lay it out stepwise in metric, I’ll pay closer attention.
 
Where does it say 5:1 in the Tripoli Safety Code? I am not arguing that it isn't in there, my version is 2012. The current one to download from the TRA website is only a few pages long showing changes. I remember seeing 3:1 in the NFPA 1127 but nothing about it in TRA codes.
In the Safe Launch Practices it says 3:1 using average thrust. As does NFPA 1127.
In the RSO guidelines it says:
Verify that the initial thrust of the motor chosen will provide at least a 5:1 thrust-to-weight ratio.
And that can be done by:
A printout from a flight prediction software package can be presented. In this case the
prediction output should indicate the thrust-to-weight of > 5, the initial acceleration of > 5
g’s, or the velocity of the rocket at the end of the rod/rail/tower > 45 f/s.

It was mentioned in the latest Tripoli Report. Looks like the wording in the Safety Code (but I still can't find it) is being changed from 5:1 average thrust to 5:1 initial thrust, as the RSO guidelines already state.

Maybe it can worded to allow 5:1 on initial thrust but keep the 45 f/s in lieu of the 5:1? Either way, all the documents should match. Not being critical, but discrepancies in the documents could lead to problems. Some people will argue over just about anything...we all know that. And we don't want trouble on the flight line.
 
MikeyDSlagle said:
Where does it say 5:1 in the Tripoli Safety Code? I am not arguing that it isn't in there, my version is 2012. The current one to download from the TRA website is only a few pages long showing changes. I remember seeing 3:1 in the NFPA 1127 but nothing about it in TRA codes.
In the Safe Launch Practices it says 3:1 using average thrust. As does NFPA 1127.
In the RSO guidelines it says:
Verify that the initial thrust of the motor chosen will provide at least a 5:1 thrust-to-weight ratio.
And that can be done by:
A printout from a flight prediction software package can be presented. In this case the
prediction output should indicate the thrust-to-weight of > 5, the initial acceleration of > 5
g’s, or the velocity of the rocket at the end of the rod/rail/tower > 45 f/s.

It was mentioned in the latest Tripoli Report. Looks like the wording in the Safety Code (but I still can't find it) is being changed from 5:1 average thrust to 5:1 initial thrust, as the RSO guidelines already state.

Maybe it can worded to allow 5:1 on initial thrust but keep the 45 f/s in lieu of the 5:1? Either way, all the documents should match. Not being critical, but discrepancies in the documents could lead to problems. Some people will argue over just about anything...we all know that. And we don't want trouble on the flight line.
Click to expand...

Mikey,
5:1 isn’t in the Tripoli Safety Code, as far as I remember. Our Safety Code consists of three separate documents. The first is NFPA 1127, where as you correctly pointed out it says 3:1 average.
The problem is exactly as you mentioned, having a consistent set of rules. While going through the L2 test and study guide we have looked at the source references and we found that they all say different things.
We’re still working on how that although I owe Chris Short some serious work and I’ve fallen behind.
 
The RSO has the final say, it's their members, cars, neighbors at risk. As Steve says a rule of thumb. Experience and simulations will make a difference. My 7.5 V-2 likes more leap off the paid, where 700 avg thrust is supposed to be around 5:1. I like to whack it with a K950, otherwise it "lays over" during the ascent.
Shortcut method: Total weight of loaded vehicle (w/ motor) x 22.5= min avg thrust you need, for 5:1
 
Last edited:
Steve Shannon said:
Mikey,
5:1 isn’t in the Tripoli Safety Code, as far as I remember. Our Safety Code consists of three separate documents. The first is NFPA 1127, where as you correctly pointed out it says 3:1 average.
The problem is exactly as you mentioned, having a consistent set of rules. While going through the L2 test and study guide we have looked at the source references and we found that they all say different things.
We’re still working on how that although I owe Chris Short some serious work and I’ve fallen behind.
Click to expand...

No worries Steve. Really not trying to nit-pick, just wasn't sure if I missed something somewhere in the text. You guys keep doing what you do. All the work behind the scenes is much appreciated.

Dave A said:
The RSO has the final say, it's their members, cars, neighbors at risk. As Steve says a rule of thumb. Experience and simulations will make a difference. My 7.5 V-2 likes more leap off the paid, where 700 avg thrust is supposed to be be around 5:1. I like to whack it with a K950, otherwise it "lays over" during the ascent.
Shortcut method: Total weight of loaded vehicle x 22.5= min avg thrust you need.
Click to expand...

My 2.6" V2 has flown once. I put it on our longer rail to be sure it had enough speed at the end. It laid over and went cruise missile. Didn't damage anything but I have since added nose weight so I can comfortably put a bigger motor in there; and electronics so I don't have to fiddle with the delay.
 
Yeah, I've never been a fan of that rule of thumb when it's so easy to get a quick estimate of speed off the launch rail. (That of course is another rule of thumb, but I guess that's the subject for another post.)

My guess is that 5:1 is just a more conservative version of 3:1, but that only begs the question of where 3:1 came from. The more conservative ratio could have come with the advent of HPR where typical APCP bates grain thrust curves have less of an initial spike. (This is just speculation on my part.)

simfile871_650x350n.png

simfile871_650x350n.png

simfile2013_650x350n.png
 
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With progressive (humped) thrust curves like on smoke motors, the average thrust is really misleading as to the actual initial liftoff thrust.

It is "easy" to estimate speed off rail, but again their are complications. How long is the rail exactly? How long till the first button is off the rail? (now your effective rail is shorter). How high does the rocket sit on the pad, is the aft button flush with rail bottom, or does it sit higher up because of the blast deflector? (Now the rail is even shorter)

As an engineer I dislike rules of thumb when designing a rocket, but once I've flown one a couple times and know the behavior, its nice to be able to pick and fly motors without running through two spreadsheets or simulations.

Remember that for general sport flying, not everyone is a rocket scientist. The rules work pretty dang well and keep the line moving smoothly instead of having each RSO check become a long technical discussion involving printouts and calculators.

Extreme projects and cert flights of course get more scrutiny as they should.
 
Nytrunner said:
With progressive (humped) thrust curves like on smoke motors, the average thrust is really misleading as to the actual initial liftoff thrust.

It is "easy" to estimate speed off rail, but again their are complications. How long is the rail exactly? How long till the first button is off the rail? (now your effective rail is shorter). How high does the rocket sit on the pad, is the aft button flush with rail bottom, or does it sit higher up because of the blast deflector? (Now the rail is even shorter)

As an engineer I dislike rules of thumb when designing a rocket, but once I've flown one a couple times and know the behavior, its nice to be able to pick and fly motors without running through two spreadsheets or simulations.

Remember that for general sport flying, not everyone is a rocket scientist. The rules work pretty dang well and keep the line moving smoothly instead of having each RSO check become a long technical discussion involving printouts and calculators.

Extreme projects and cert flights of course get more scrutiny as they should.
Click to expand...
"Remember that for general sport flying, not everyone is a rocket scientist. The rules work pretty dang well and keep the line moving smoothly instead of having each RSO check become a long technical discussion involving printouts and calculators."

Bingo! Probably the best reason yet for this particular "rule of thumb".
 
rharshberger said:
"Remember that for general sport flying, not everyone is a rocket scientist. The rules work pretty dang well and keep the line moving smoothly instead of having each RSO check become a long technical discussion involving printouts and calculators."

Bingo! Probably the best reason yet for this particular "rule of thumb".
Click to expand...

Exactly. That’s what I meant (but didn’t say as clearly) when I said this:
It’s just a rule of thumb that saves RSOs from requiring that every flyer justify their motor choice by providing a simulation.
Click to expand...
 
in the simplified equations, i.e. no drag or rod friction forces,
and if you consider constant or average values during the interval of time while the rocket is on the launch rod...

d = 0.5*a*t^2

a = V/t, or t=(V/a) substituting into d equation:

d = 0.5*a*(V/a)^2 = 0.5*V^2/a

so speed at the end of the rod is
V=sqrt(2*a*d)

where a = (T/W - 1)g, from the Thrust-Weight=ma Force equation.

So, a very simplified equation for speed at the end of a rod of height d, is

V = sqrt[2*(T/W - 1)*g*d]

where g is the gravitational acceleration, 9.8m/s^2 or 32.17ft/s^2

Note: acceleration-to-gravity ratio is (a/g) = (T/W-1), or one less than the thrust-to-weight ratio.

The dynamic computer simulation is more accurate and uses more values from the engine thrust curve, but this simple form shows the relationship between the various parameters in a more intuitive form. An acceptable V at the end of the rod depends on wind speed as well.

Engines are usually rated by peak thrust or average thrust, not the average thrust in the time interval while on the launch rod, which is the T in the simple equations above, so you have to have some knowledge of the thrust curve to use an appropriate number for T/W, there is some variability in the different type of engines with respect to how quickly they get to their peak/avg thrust value as shown in the posts above.
 
Hi everyone,

As a result of your useful replies to my original question, I am now able to make some useful calculations. GlenP's last post was quite helpful.

In a few months, I am hoping to buy and build an Apogee Peregrine, so I have been running simulations using RockSim.

I am testing a J-300 motor, and the loaded rocket has a mass of 2.767 kg. Thus, the weight is (300 Newtons) / [ (2.767 kg) (9.91 m/s^2) ], which yields a Thrust:Weight ratio of approximately 11.1.

Next I will calculate the velocity using the formula derived by GlenP and others in this thread. On the RockSim program, my launch guide measures 2 meters. Putting everything together comes up with the following equation:

velocity = √ [ 2 * gravity * (Thrust/Weight - 1) * (2 meters) ] = √ [ 2 * (9.81 m/s^2) * (11.1 - 1) * (2 m) ] = approximately 20.9 m/s.

RockSim gives a velocity off the launch guide of 23.9 m/s, and those two numbers are quite close. Moreover, both of those numbers are well above the minimum launch-guide velocity of approximately 15.5 m/s.

While working all of this out, it occured to me that we could use the formula velocity = √ [ 2 * gravity * (T/W - 1) * (launch-guide distance) ] to solve for T/W or for launch-guide distance.

I appreciate all the helpful replies to my original question.

Stanley
 
Last edited:
rharshberger said:
"Remember that for general sport flying, not everyone is a rocket scientist. The rules work pretty dang well and keep the line moving smoothly instead of having each RSO check become a long technical discussion involving printouts and calculators."

Bingo! Probably the best reason yet for this particular "rule of thumb".
Click to expand...
Hopefully most RSOs alreay know which rocketeers they can trust, and give a quick inspection and pass, whereas new, inexperienced, unknown persons get a little more scrutiny. Knowing which rocketeers have already proven time and again that they know what they're doing can speed the lines up significantly.
 
Bat-mite said:
Hopefully most RSOs alreay know which rocketeers they can trust, and give a quick inspection and pass, whereas new, inexperienced, unknown persons get a little more scrutiny. Knowing which rocketeers have already proven time and again that they know what they're doing can speed the lines up significantly.
Click to expand...
Definitely, we are a small enough group at most regional launches that the questionable fliers are known....
 

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