## Modelling solid rocket engine propellant mass/time curve

### Modelling solid rocket engine propellant mass/time curve

I'm developing a mathematical model of model solid rocket engine
behavior. There's plenty of thrust/time curves available, but no
mass/time curves that I'm aware of for model engines.

Currently I'm assuming that propellent mass varies linearly over
the burn time of the engine. This strikes me as only being realistic
for a pure end-burner propellant grain, and I'm looking for a better
model of this behavior that applies to all grain configurations.

Would a better approximation be to make mass decrease proportionally
to the ratio of the integral of thrust/time over total impulse? This
would assume that basically more thrust -> more propellant burned. I
am unsure if this is the correct physics (for instance, pressure plays
a large role as well). I am trying to develop as accurate as possible
a model given the typical data available for model rocket engines.

This is what I'm thinking of trying:

cmass = casing mass
pmass = propellant mass
t = time
F(t) = force at time t
Integral from 0 to t F(t) dt
mass(t) = cmass + pmass - pmass * ----------------------------
total impulse

Is this what WRASP, etc. use? Any other suggestions?

----------------------------------------------------------------------
spam.

### Modelling solid rocket engine propellant mass/time curve

Quote:

> I'm developing a mathematical model of model solid rocket engine
> behavior. There's plenty of thrust/time curves available, but no
> mass/time curves that I'm aware of for model engines.

None known here, either.  Kinda difficult to 'get', actually <g>.

Quote:
> Currently I'm assuming that propellent mass varies linearly over
> the burn time of the engine. This strikes me as only being realistic
> for a pure end-burner propellant grain, and I'm looking for a better
> model of this behavior that applies to all grain configurations.

> Would a better approximation be to make mass decrease proportionally
> to the ratio of the integral of thrust/time over total impulse?

I would think so.  I did some 'modeling' back in the mid 80s that did
basically the same thing.

Quote:
> This
> would assume that basically more thrust -> more propellant burned. I
> am unsure if this is the correct physics (for instance, pressure plays
> a large role as well).

'Pressure' plays a role in burn rate -- but, also, Specific Impulse
(generally directly proportional) -- which would lend justification to
your concerns, as a higher pressure results in better 'ooomph' per
pound.

One thing's for sure - taking the integral approach is FAR more accurate
than a 'linear' one.  You might could add the capability of varying
I(sp) as proportional to instantaneous thrust.  Maybe some of the
'engineers' will chime in with some valid ranges (I'm thinking 50 to 250
as a start).

Quote:
> I am trying to develop as accurate as possible
> a model given the typical data available for model rocket engines.

> This is what I'm thinking of trying:

> cmass = casing mass
> pmass = propellant mass
> t = time
> F(t) = force at time t
>                                   Integral from 0 to t F(t) dt
> mass(t) = cmass + pmass - pmass * ----------------------------
>                                          total impulse

> Is this what WRASP, etc. use? Any other suggestions?

-- john.

"Once you give up your ignorance, you can't ever get it back."
Unknown

### Modelling solid rocket engine propellant mass/time curve

Quote:

> Thats not true even for pure end burning grains. This is because,
> even small diameter end burning grains actually start with a flat
> face, but that flat face starts to cone after a few seconds of burn.

That's my understanding, as well, Brian.

-- john.

### Modelling solid rocket engine propellant mass/time curve

Quote:

>>Currently I'm assuming that propellent mass varies linearly over
>>the burn time of the engine. This strikes me as only being realistic
>>for a pure end-burner propellant grain, and I'm looking for a better
>>model of this behavior that applies to all grain configurations.

>Thats not true even for pure end burning grains. This is because, even small
>diameter end burning grains actually start with a flat face, but that flat face
>starts to cone after a few seconds of burn. Though the model for all other
>grains should be rather easy......simple goemetric equations....

Yes, except the information for the geometry of model rocket engines isn't
readily available. That is why I am attempting to model it via the thrust-
time curve, which is information that is readily available.

### Modelling solid rocket engine propellant mass/time curve

Quote:

> I'm developing a mathematical model of model solid rocket engine
> behavior. There's plenty of thrust/time curves available, but no
> mass/time curves that I'm aware of for model engines.

> Currently I'm assuming that propellent mass varies linearly over
> the burn time of the engine. This strikes me as only being realistic
> for a pure end-burner propellant grain, and I'm looking for a better
> model of this behavior that applies to all grain configurations.

> Would a better approximation be to make mass decrease proportionally
> to the ratio of the integral of thrust/time over total impulse? This
> would assume that basically more thrust -> more propellant burned. I
> am unsure if this is the correct physics (for instance, pressure plays
> a large role as well). I am trying to develop as accurate as possible
> a model given the typical data available for model rocket engines.

Most of the rocket altitude simulators seem to just divide the
propellent mass into equal chunks for each interval of the burn time.
For motors with fairly constant thrust this works without any
discernable error.

For a more accurate simulation of propellant mass try the following.
The reaction force of a rocket motor is roughly the mass of the
expelled gas times the exhaust velocity (Ve).  If the motor burns with
a constant Ve, then the lost mass is proportional to the impulse
during the time interval.  In other words, take the average thrust
during an interval, multiply times the delta-t, to get the interval
impulse. Then divide by the total impulse of the motor. This is the
percentage of mass lost in that time interval.  With a constant delta-t,
the "mass-time" curve will have the shape of the thrust-time curve.

-John DeMar
NAR 52094
http://web.syr.edu/~smdemar/rocketry.htm

### Modelling solid rocket engine propellant mass/time curve

Quote:
>Currently I'm assuming that propellent mass varies linearly over
>the burn time of the engine. This strikes me as only being realistic
>for a pure end-burner propellant grain, and I'm looking for a better
>model of this behavior that applies to all grain configurations.

Thats not true even for pure end burning grains. This is because, even small
diameter end burning grains actually start with a flat face, but that flat face
starts to cone after a few seconds of burn. Though the model for all other
grains should be rather easy......simple goemetric equations....

Cheers,

Brian

### Modelling solid rocket engine propellant mass/time curve

Yes, except the information for the geometry of model rocket engines isn't
readily available. That is why I am attempting to model it via the thrust-
time curve, which is information that is readily available.

There's an article in a recent issue of "Journal of Pyrotechnics" that goes
into gruesome detail of the burn geometry of the early stages in the burn of
a typical black powder model rocket motor.  A search at www.rocketryonline.com
will point to to JoP.

BillW
--
(remove spam food from return address)

### Modelling solid rocket engine propellant mass/time curve

Quote:

> I'm developing a mathematical model of model solid rocket engine
> behavior. There's plenty of thrust/time curves available, but no
> mass/time curves that I'm aware of for model engines.

> Currently I'm assuming that propellent mass varies linearly over
> the burn time of the engine. This strikes me as only being realistic
> for a pure end-burner propellant grain, and I'm looking for a better
> model of this behavior that applies to all grain configurations.

Perhaps a better assumption would be that propellant mass varies with the
motor thrust. A non flat motor is burning more propellant when it's putting
out more thrust. Compute the specific impulse. Compute the thrust for the
time interval being integrated. From that you can compute the propellant
mass burned off in that interval.

Bob Kaplow      NAR # 18L       TRA # "Abort, Retry, Fail?"

### Modelling solid rocket engine propellant mass/time curve

Quote:
>I'm developing a mathematical model of model solid rocket engine
>behavior. There's plenty of thrust/time curves available, but no
>mass/time curves that I'm aware of for model engines.

I too have been trying to develop that information for a dynamic
stability program that I've been writing. It would even be helpful to
know just where the center of gravity of an engine is before firing.
The casing characteristics can be obtained from a spent engine. But
where to actually place the CG of the engine is a guess until you have
one in hand.
The models that I developed use 3 components: casing, delay
(if required), and propellent. After REALLY getting bogged down in
grain-burning theory, I felt that for my application I could get
accurate enough results by, well, making a educated guess.
So, for a simple end-burner I use a 45 or 60 deg. cone moving forward,
depending on the depth of the 'dimple'. The cone expands to 180
deg.(flat flame front) depending on the shape of the thrust curve.
For core-burners,C-slots or similar, I use a fulcum of a 6 deg. cone
moving out and forward with no angular expansion.

no correction for pressure,heat, erosion, ect.
The delay charge burns at a constant forward rate.
I do not make any pretense of the accuracy of this: just that the CG
and inertia of the engine will most likely follow something pretty
similar. (I hope, until I learn otherwise)

<snip a bunch>

Quote:

>Is this what WRASP, etc. use? Any other suggestions?

wRASP uses the method; mass used= Impulse used /Isp
under the thrust / time curve. (.01 sec. slices I think)
Isp= Itotal / Weight Propellent
Any CAD type packages I've seen don't get involved other than
engine being a point source.

If you do get some decent models going, please let me know.
Otherwise sunsite does have some programs on grain/engines in the
rocketry section.
Good luck.

remove the spam.
"spammers are killing all this"

### Modelling solid rocket engine propellant mass/time curve

Sorry, I cannot offer help -- just further complication:

Does anyone have a good approximation for temperature effects on thrust?

This has been of particular interest to me as I look forward to several
sub 20-deg F launches this winter.  Ideally, a version of WRASP that
incorporates launch temperature to adjust the thrust curve would be
great, although this would have to be a simple approximation. I believe
WRASP currently uses the temp input for air density only.

Does anyone have any low-temp thrust data??

F. Urban

### Modelling solid rocket engine propellant mass/time curve

Quote:

>I'm developing a mathematical model of model solid rocket engine
>behavior. There's plenty of thrust/time curves available, but no
>mass/time curves that I'm aware of for model engines.
>Currently I'm assuming that propellent mass varies linearly over
>the burn time of the engine. This strikes me as only being realistic
>for a pure end-burner propellant grain, and I'm looking for a better
>model of this behavior that applies to all grain configurations.

The program "Motorsim" (by Gary Crowell; nice bit of software Gary!!)
will plot thrust vs. time for several motor configurations, and has
the option of also plotting propellant mass.  Unfortunately it doesn't
have a database of commercial motors.  But it will give you an idea of
mass-time variation for different motor configurations.  Which does
mirror the thrust-time variation.

It models endburner, cored endburner, cylindrical core, D-slot, and
star grain.  It's shareware (IBM DOS) and I think it's available at
Sunsite.  If not, e-mail me.

P'rfesser
"I'm a professor, but I don't play one on TV"

### Modelling solid rocket engine propellant mass/time curve

Quote:

>> I'm developing a mathematical model of model solid rocket engine
>> behavior. There's plenty of thrust/time curves available, but no
>> mass/time curves that I'm aware of for model engines.

>> Currently I'm assuming that propellent mass varies linearly over
>> the burn time of the engine. This strikes me as only being realistic
>> for a pure end-burner propellant grain, and I'm looking for a better
>> model of this behavior that applies to all grain configurations.

>> Would a better approximation be to make mass decrease proportionally
>> to the ratio of the integral of thrust/time over total impulse? This
>> would assume that basically more thrust -> more propellant burned. I
>> am unsure if this is the correct physics (for instance, pressure plays
>> a large role as well). I am trying to develop as accurate as possible
>> a model given the typical data available for model rocket engines.

>  Most of the rocket altitude simulators seem to just divide the
>propellent mass into equal chunks for each interval of the burn time.
>For motors with fairly constant thrust this works without any
>discernable error.

>  For a more accurate simulation of propellant mass try the following.
>The reaction force of a rocket motor is roughly the mass of the
>expelled gas times the exhaust velocity (Ve).  If the motor burns with
>a constant Ve, then the lost mass is proportional to the impulse
>during the time interval.  In other words, take the average thrust
>during an interval, multiply times the delta-t, to get the interval
>impulse. Then divide by the total impulse of the motor. This is the
>percentage of mass lost in that time interval.  With a constant delta-t,
>the "mass-time" curve will have the shape of the thrust-time curve.

>  -John DeMar
>  NAR 52094
>  http://web.syr.edu/~smdemar/rocketry.htm

I'm not sure what your final application of this model is for (but I
assume it's for a sim of a rocket flight...), but it's likely that the
error you introduce from assuming a linear burn rate (or the above better
approach) is smaller than other uncertainties in the calculations anyway.
Since proppellant weight is (usually) a (fairly) small fraction of total
rocket weight, a 20 or 25% error on propellant mass during a short period
of time probably wouldn't be as large an effect as a 3 or 4 % error in
drag
coefficient or something similar (and more likely).

This is just my first impression, and not meant to discourage you from
improving your calculations. In fact I'd be very interested in how your
results change when you go from using a linear mass loss to a proportional
to thrust mass loss. Could you post the results if you ever do it???
Computer modelling is something I enjoy and do quite a bit of.

Regards,

Jeff Bezaire

--

### Modelling solid rocket engine propellant mass/time curve

My simulation spreadsheet, rocket.xls, does some simple mass/time
calculations based on burn time.  Check it out at
http://www.olywa.net/tomm/simulate.htm.

Quote:

>>I'm developing a mathematical model of model solid rocket engine
>>behavior. There's plenty of thrust/time curves available, but no
>>mass/time curves that I'm aware of for model engines.

>I too have been trying to develop that information for a dynamic
>stability program that I've been writing. It would even be helpful to
>know just where the center of gravity of an engine is before firing.
>The casing characteristics can be obtained from a spent engine. But
>where to actually place the CG of the engine is a guess until you have
>one in hand.
> The models that I developed use 3 components: casing, delay
>(if required), and propellent. After REALLY getting bogged down in
>grain-burning theory, I felt that for my application I could get
>accurate enough results by, well, making a educated guess.
>So, for a simple end-burner I use a 45 or 60 deg. cone moving forward,
>depending on the depth of the 'dimple'. The cone expands to 180
>deg.(flat flame front) depending on the shape of the thrust curve.
>For core-burners,C-slots or similar, I use a fulcum of a 6 deg. cone
>moving out and forward with no angular expansion.

>no correction for pressure,heat, erosion, ect.
> The delay charge burns at a constant forward rate.
>I do not make any pretense of the accuracy of this: just that the CG
>and inertia of the engine will most likely follow something pretty
>similar. (I hope, until I learn otherwise)

><snip a bunch>

>>Is this what WRASP, etc. use? Any other suggestions?

> wRASP uses the method; mass used= Impulse used /Isp
>under the thrust / time curve. (.01 sec. slices I think)
>Isp= Itotal / Weight Propellent
> Any CAD type packages I've seen don't get involved other than
>engine being a point source.

> If you do get some decent models going, please let me know.
>Otherwise sunsite does have some programs on grain/engines in the
>rocketry section.
> Good luck.

>remove the spam.
>"spammers are killing all this"

### Modelling solid rocket engine propellant mass/time curve

For the record, rasp.c does depreciate mass linearly, primarily (I suppose)
because RASP79E.BAS did. It's an unnecessarily coarse approximation. Most
other simulators depreciate mass according to expended impulse, as several
folks have described. That's is an excellent approximation. Not sure why RASP
has never been changed. It's easy to do.

You can compute, in theory, how much mass is being expended. I have a motor
simulator that predicts on the basis of an Isp/chamber pressure graph, which
I happened to have available for a breed of black powder motors. Chamber
pressure (equilibrium chamber pressure) can be computed from the ratio of
propellant surface area to nozzle throat area. Propellant burning rate can be
computed from chamber pressure. The net result is that the impulse-
proportional method (proportionality is effective exhaust velocity) over-
estimates mass loss slightly in thrust peaks, and underestimates it slightly
in thrust troughs.

From what I've seen, the difference is small in all cases. It's smallest in
motors with more level thrust curves.

-Larry (Don't sweat it) C.

### Modelling solid rocket engine propellant mass/time curve

Quote:

>I'm developing a mathematical model of model solid rocket engine
>behavior. There's plenty of thrust/time curves available, but no
>mass/time curves that I'm aware of for model engines.

>Currently I'm assuming that propellent mass varies linearly over
>the burn time of the engine. This strikes me as only being realistic
>for a pure end-burner propellant grain, and I'm looking for a better
>model of this behavior that applies to all grain configurations.

>Would a better approximation be to make mass decrease proportionally
>to the ratio of the integral of thrust/time over total impulse? This
>would assume that basically more thrust -> more propellant burned. I
>am unsure if this is the correct physics (for instance, pressure plays
>a large role as well). I am trying to develop as accurate as possible
>a model given the typical data available for model rocket engines.

>This is what I'm thinking of trying:

>cmass = casing mass
>pmass = propellant mass
>t = time
>F(t) = force at time t
>                                  Integral from 0 to t F(t) dt
>mass(t) = cmass + pmass - pmass * ----------------------------
>                                         total impulse

The mass, thrust, acceleration, velocity and displacement with respect to time
(t) would be solved for using a differential equation, not an integral.