Acceleration curve fitting.

[Notebook]

I'm starting to find a function to match a Blue Streak F1 acceleration graph. This is the starting Mathcad document.

http://i89.photobucket.com/albums/k207/Notebook_04/CurveFit_1_.jpg

http://i89.photobucket.com/albums/k207/Notebook_04/CurveFit_2_.jpg

I'd like to get the end points closer (especially the cut-off value!)to the document's values before using Mathcad's curve-fit functions.
Besides adjusting the thrust for altitude, and atmospheric drag, any other variables I should model at this early stage?

Many thanks,N.

 

[tblaxland]

Did the engine throttle? It is the only thing I can image to account for the lower max acceleration. Either that or very poor residuals.

 

[simonpro]

What equation are you using for the altitude thrust adjustment?

 

[Notebook]

Did the engine throttle? It is the only thing I can image to account for the lower max acceleration. Either that or very poor residuals.

The real engine didn't throttle, it was constant thrust.

I have
Lift Off Acceleration 11.8m/sec^2 from documentation, and 13.4m/sec^2 from Mathcad.

That dosent bother me too much at the moment, its the cut-off acceleration!
64.7m/sec^2 versus 234m/sec^2 from Mathcad.

But its early days...

N.





---------- Post added at 13:18 ---------- Previous post was at 13:11 ----------

What equation are you using for the altitude thrust adjustment?

None at the moment, its 1334kN all the way; that was my next question!

If take the "Vacuum thrust" to be at 100Km? then if engine cut-off is at 54Km, I could just model it as 1/2 the vacuum figure, and interpolate between the two values.

N.

 

[simonpro]

None at the moment, its 1334kN all the way; that was my next question!

If take the "Vacuum thrust" to be at 100Km? then if engine cut-off is at 54Km, I could just model it as 1/2 the vacuum figure, and interpolate between the two values.

Well, it wouldn't be half as the atmospheric pressure is not linear.

The correct equation to use is:

F = mdot*ve + Ae*(pe-pa)

With
mdot = massflow rate
ve = exhaust velocity
Ae = exhaust area
pe = exhaust pressure
pa = atmospheric pressure

Exhaust area can be calculated from the nozzle diameter and exhaust pressure from the vacuum thrust figure. Remember that there were two engines for Blue Streak, so the thrust is doubled.

 

[BrianJ]

Funnily enough, you get a pretty good fit to the acceleration graph if you assume a throttle setting of 84%(Sea Level Thrust) all the way, leaving 16% fuel at cut-off.

I assume you've found this document?
http://www.spaceuk.org/bstreak/bs/f1.htm

Not easy to disentangle the numbers since the flight didn't end as planned.

Good luck,
Brian

 

[Notebook]

Thanks Simonpro, I'll have a go at that.
I gave the total thrust for the two engines, guess I'll have to model them correctly to use that formula

N.

---------- Post added at 14:20 ---------- Previous post was at 14:01 ----------

Funnily enough, you get a pretty good fit to the acceleration graph if you assume a throttle setting of 84%(Sea Level Thrust) all the way, leaving 16% fuel at cut-off.

I assume you've found this document?
http://www.spaceuk.org/bstreak/bs/f1.htm

Not easy to disentangle the numbers since the flight didn't end as planned.

Good luck,
Brian

Thanks for that Brianj and quick work! That is a good site for BS, and the book is good too.
It can get confusing seperating performance figures from the missile version and the Europa version. Helps that the missile is usually Imperial, and Europa SI.
As F1 had a fuel slosh eco, and didn't get above 40km under thrust, I'm assuming the figures I'm using are for a later flight. As the thrust(2 engines) is given as 1344KN, I'm assuming its a missile standard, the engines were uprated for the Europa.

What could possibly go wrong with those assumptions...
N.

 

[simonpro]

Thanks Simonpro, I'll have a go at that.
I gave the total thrust for the two engines, guess I'll have to model them correctly to use that formula

Just double the exhaust area and it'll work fine.


Also, have you checked the astronautix page? Their numbers are usually pretty accurate, but differ from yours:
http://www.astronautix.com/engines/rz2.htm

---------- Post added at 06:13 PM ---------- Previous post was at 06:09 PM ----------

Two other things:

1) Your empty vehicle mass on slide 2 doesn't match the value given on slide 1 (5680kg - 6168kg)

2) The reason your cutoff acceleration is too high is because you haven't included the upper stage masses. If you include those then the calculated acceleration will be closer (60m/s/s).

 

[Notebook]

Thanks Simonpro, just doing the one engine, so I'll double up when it goes into BS. I've seen those figures, I think thats the uprated version for Europa.
There dosen't seem to be a designation for the later model, they all seem to be called RZ-2! I'll stick with the 667KN figure for the F1.

Worried about the exhaust diameter, I've measured it at 1.1m from drawings, so that needs checking.

thanks, N.

Just seen points 1) and 2), I'll have a look.

---------- Post added at 17:33 ---------- Previous post was at 17:17 ----------

Re points 1) and 2)

Both related,I'm modelling the F1 missile variant, so no second/third stages as Europa.
However it did have a payload! Forgot that, explains why my empty mass is wrong.
Just need a mass for the nuclear warhead...

N.

 

[BrianJ]

Hmmmm, this has been niggling at me all afternoon....are you sure that acceleration graph is for the F1 flight? It would make more sense if it were for the Europa II 4-stage version (as per simonpro's point 2)
http://www.astronautix.com/lvs/europa.htm

No need to assume strange throttle settings and 16% fuel remaining at cut-off, if it were.

Never underestimate other people's capacity to give you the wrong numbers :-D

Just thought I'd mention it...
Brian

 

[Notebook]

I'm not sure that graph is for the missile variant, its just the circumstantial evidence as above. I'm using this :
http://www.bis-spaceflight.com/sitesia.aspx/page/128/Node/108/l/en-us
Blue Streak by Charles Martin. (bottom of frame)

Lots of info, but he does hop between the different vesions, and it isn't always clear which variant is being referenced.

I can only make a best opinion, and see how the figures come out.

Should get more sane figures when I find a mass value for the nuke.

N.

 

[simonpro]

Sorry, I didn't realise you were modelling the missile version. Anyway, the mass of a typical nuke (I think bklue streak was designed for 1MT weapons) would be about 800-1000kg.

The acceleration of 234m/s/s is also not unlikely for a missile system. Iirc, Trident burns out at around half that.

 

[Notebook]

I've put 1000Kg in for a payload, and as you'd expect it comes down to 170m/s/s at eco. I'm using some figures for your equation, when I get confident with them, I'll put the next slide up...
It means a detour to get pa(t) values for the flight; might as well use the Orbiter atmospheric pressure formula, p39., API Guide?

N.

N.

---------- Post added at 17:42 ---------- Previous post was Yesterday at 20:08 ----------

Quite a detour...

http://i89.photobucket.com/albums/k207/Notebook_04/img022.jpg

I've broken the altitudes into three segments, and working on the zero to 10Km part.
The equation works for these static variables, had to rename R and T, Mathcad complains about renaming "Rankine" and "Tesla"!

I need T and T(h), I've took T to be 288K, how do I find T(h)?

All answers appreciated, N.

---------- Post added at 22:25 ---------- Previous post was at 17:42 ----------

Just realised I've miss-understood the pressure equation, and the temp/alt graph. So the above questions don't make sense.

When I've got a better grasp, I'll be back when I sort this out.

N.

 

[simonpro]

I'd suggest downloading the latest public beta and checking out the "earth_atm.pdf" technote, it explains it all pretty well. Probably a bit too complex for a study in mathcad, but it's still worth a read.
Alternatively if you have matlab you can just get orbiter to spit out the atmospheric parameters in realtime, which would ensure a good fit to the orbiter world. Let me know if you don't have matlab, it's a slow day at work today (two of our satellites are being moved, so are offline) so maybe i can cobble something together to output the data.

 

[Notebook]

Thats very decent of you Simonpro, I'll have a look at that documentation, and see how far I get. I have the student version of Maple13, but not on this PC. Can't get into Maple, its a bit "strict" compared to Mathcad...

Many thanks, N.

 

[simonpro]

Maple is a pain in the ass. I've never used mathcad but from what I've heard it's a bit of a pain too.
IMO, matlab and IDL are the best suited to this type of thing. Both are more like programming languages, but once you get used to that they both have tremendous power.
Trying to get IDL to output exactly the same thing twice, though, is problematic

 

[Notebook]

Mathcad is a bit "quick and dirty", so its useful for what I do with it... Maple seems heavier, but I can't get into its presentation, it seems to repeat everything I put in, I put in, and then sits there looking at me.
Looked at Matlab, but they aren't convinced of my student status(can't say I blame them), so its commercial price is out of question for me, don't know IDL.

The earth_atm.pdf is interesting, but luckily for me, these new models seem to come in over 90Km altitude. I say lucky, as the RZ-2 didn't get above much above 90Km before eco so I can use the simpler equations.
Below 90K is probably a good starting point for this exercise.
I think I'll put the acceleration curve-fit on hold till I get a model for the RZ-2 thrust/altitude performance with the standard atmosphere model, and save the new ones for Europa.

N.

---------- Post added at 18:12 ---------- Previous post was at 15:38 ----------

Bit more stuff.

This is what I get for the atmospheric pressure versus altitude up to 10km.

http://i89.photobucket.com/albums/k207/Notebook_04/RZ2_thrust-alt_1.jpg

and this is for the RZ2 engine when the pressure/alt is applied to the thrust formula.

http://i89.photobucket.com/albums/k207/Notebook_04/RZ2_thrust-alt_2.jpg

I think they look at least the right shape.

N.

---------- Post added at 08:52 ---------- Previous post was Yesterday at 18:12 ----------

A couple of questions about the atmoshere equation:-

p(h) = p1(T(h)/T)-g0/( a * R ).

1)
For the term "a"(Temperature Gradient), I used
a = 288K-216K/10000m , that is the starting temp at ground level is 288K, and at 10Km it is 216K.
This gives 7.2e-3K/m.
I think this should be negative, but doing this gives a very ugly expression for the pressure at 10Km

(-4.872*10^5+4.957i*10^5)*Pa; it seems to have wandered off into imaginary world?

Leaving it positive gives 264.977*Pa at 10Km.

2)
This is more fundamental, I'm using the "a" term to find the T(h) value during the iterations. Not sure this is correct, should I be using some other method?

All replies welcome, N.

 

[starbird]

According to ICAO, troposphere goes up to 11km, not 10km. (I haven't actually looked in the orbiter docs to see how martin does it)

Your temperature gradient should just be -6.5 Kelvin per km. So at 10km the temperature is -6.5*10 = 233.15 . If you wanted a formula it would be

T(h)=288.15 - ((288.15-216.65)/11 km)*(1000*h) (assuming h is meters)

Once you find temperature, you can plug that into your pressure equation. Your a variable in the pressure formula should just be

a=-((288.15-216.65)/11000)

Or just -6.5e-3 K/m

edit

Looking closer at your worksheet, the only thing that looks incorrect is the cutoff altitude of 10km. At 10km you should be getting 223.15K and a pressure of 2.64e4 Pa.

 

[tl8]

Mathcad is a bit "quick and dirty", so its useful for what I do with it... Maple seems heavier, but I can't get into its presentation, it seems to repeat everything I put in, I put in, and then sits there looking at me.
Looked at Matlab, but they aren't convinced of my student status(can't say I blame them), so its commercial price is out of question for me, don't know IDL.

Tried Scilab?

 

[Notebook]

According to ICAO, troposphere goes up to 11km, not 10km. (I haven't actually looked in the orbiter docs to see how martin does it)

Your temperature gradient should just be -6.5 Kelvin per km. So at 10km the temperature is -6.5*10 = 233.15 . If you wanted a formula it would be

T(h)=288.15 - ((288.15-216.65)/11 km)*(1000*h) (assuming h is meters)

Once you find temperature, you can plug that into your pressure equation. Your a variable in the pressure formula should just be

a=-((288.15-216.65)/11000)

Or just -6.5e-3 K/m

edit

Looking closer at your worksheet, the only thing that looks incorrect is the cutoff altitude of 10km. At 10km you should be getting 223.15K and a pressure of 2.64e4 Pa.

Thanks for that Starbird.
To be honest, I just eyeballed it from the alt/temp graph in the API_Guide, and chopped the first segment at 10Km as a nice round number, technical, what?

I'll have a go with your commets and see what comes out.

Thanks, N.

---------- Post added at 09:21 ---------- Previous post was at 09:14 ----------

Tried Scilab?

I tries Scilab some time ago, and its impressive. It had a text type input, so was a bit daunting.
The thing with Mathcad is its a very "open" format, you can mix maths regions, and text regions on the same page. Usefull for keeping notes, and references while you are working. Suits the way I work, which is a bit "on the fly" till I get a grip on the process, and then I can tidy it up.
I haven't looked at Scilab for a few years, will check it out.

Thanks, N.

---------- Post added at 11:44 ---------- Previous post was at 09:21 ----------

Redid the variables with the standard atmosphere, as Starbirds's suggetsion

http://i89.photobucket.com/albums/k207/Notebook_04/RZ2_thrust-alt_3_.jpg

seems to fit?

N.