Calculating ballistic trajectories

[Jon]

I've been trying to figure out how to do this for a while. What I want to do is depart from one location on earth then do a
sufficient burn so I can coast thru space to my destination in the DGIII. A good model of this is a ballistic missle. Is this
possible, considering things like G force and reentry angles? If it's possible, how do I do such calculations? I have a basic
background in ballistics, but I don't know how to account for the curvature of the earth. Is there a calculator program that
can do this very thing? Thanks in advance.

[StarLost]

Jon, suborbital flight is not usually Orbiter's forte. I would recommend that you ask this question in the M6 Space Math and
Physics Forum and direct it specifically at the Mercury 5 boys. I think they might help you faster. In the meantime I think I
have some software that will help you. I'll have to check, find it and verify it for you.

(editted) Some time ago jarmonik produced a basesynchronize mfd. It is now part of his Interplanetary mfd. It might help if it can be used on a suborbital basis. Again, look for it on M6 (Addons forum).

Ken



Post Edited ( 06-20-05 05:24 )

[JimmyDean]

Jon, quite a while ago I developed a DG-III suborbital flight plan from Mojave to Cape Canaveral using Jarmonik's base sync
mfd for guidance.  I used the good old "trial and error" method, refining my burn time and climb angle until I dropped on top
of the base with some energy to spare (sometimes).  It helped me understand orbital reentries much better.

It's in one of my old notebooks.  If you'd like, I'll try and dig it up.

Interestingly enough, I tried to reverse the flight plan the other way from the cape to mojave and as I suspected, because of
the rotation of the earth, i overflew mojave by quite a distance!  But boy was it fun!

[StarLost]

Hey, JimmyDean,

if you don't mind, how about digging them out and posting them (or at least send me a copy). I've had ever so much trouble
trying to get the DG3 from KSC to Kourou on one hop.  Trial and error, to be sure ... but mostly error. I'd like to see how
you accomplished your hop.

[JimmyDean]

Hi StarLost,

I don't mind at all!  I found my notes and had a chance to try out a flight and ended up cooking my glider!  I want to figure
out what's wrong with my procedure before I post it.

I know what you mean about mostly error... it took me quite a few test flights to get it right the first time.  But I
remember I was able to consistently reproduce the flight complete with deadstick landing!  I imagine that by the time I got
around to documenting my procedure I was doing something out of habit that I forgot to write down.

I really enjoy this suborbital hop, it's about 45 solid minutes of hand-on-the-stick flying from start to finish!

Anyway, I'll have a chance this weekend to refine the flight plan, type it up, and post it here along with my scenario file.

[StarLost]

Thanks man ...  you're a one !!

[Simonpro]

Buy Fundamentals of Astrodynamics by Bate, Mueller and White - it's got a good few chapters on it as far as i recall...

[StarLost]

Simonpro wrote:
Buy Fundamentals of Astrodynamics by Bate, Mueller and White - it's got a good few chapters on it as far as i recall...

Simon, thanks for popping in on this one. I remembered that book from some other discussion and couldn't locate a copy, or
remember its name, at the time. (I know, try Amazon at about $100 US).

My son was looking for a particular astrodynamics resource (he's taking a crack at programming a true and accurate model of
our galaxy). Must have plenty of time on your hands these days as an officer in the Air Force.

I'll pass the referent on to him. Thanks again.

Oh, brings up another question that you might be able to answer for me too, Simon.  In Sol system, we reference all
coordinates (polar coordinates) to the sun as origin and to the First Point of Aries. On the galactic level, point of origin
appears to be Sagitarrius A (prime), but what is the galactic equivalent to the First Point of Aries?

[Simonpro]

Sorry i didn't reply sooner, was away.

Anyway, that's not it! BMW is a cheap ass ($10) book that just covers the very very very basics. It doesn't deal with
astronomical things such as galaxies, it focusses solely on launchers and spacecraft dynamics, iirc. There's plenty of
other books out there that cover the same material in much greater depth, though. Perhaps you've found one of
these in the past...

And on your question: Havn't got a clue :p
I'm a rocket scientist, not an astronomer. If i get a chance i'll pass it on to one of the people at uni, though - see
what they make of it
Will get back to you later in the week on that one :D

[JimmyDean]

Hi StarLost,

Sorry it took me a bit longer to prepare this than I thought.  Real life keeps intruding on my Orbiter time!

Here it is as promised.

Scenario: dg3-mojave-suborbita.scn

----- SNIP -----

BEGIN_DESC
Mojave Spaceport.
Deltaglider III suborbital test flight from Mojave to Cape Canaveral.
END_DESC

BEGIN_ENVIRONMENT
  System Sol
  Date MJD 53177.656255787
END_ENVIRONMENT

BEGIN_FOCUS
  Ship GL-30
END_FOCUS

BEGIN_CAMERA
  TARGET GL-30
  MODE Extern
  TRACKMODE TargetRelative
  FOV 50.00
END_CAMERA

BEGIN_HUD
  TYPE Surface
END_HUD

BEGIN_MFD Left
  TYPE Surface
END_MFD

BEGIN_MFD Right
  TYPE Launch
END_MFD


BEGIN_SHIPS
ISS:ProjectAlpha_ISS
  STATUS Orbiting Earth
  RPOS -6487359.16 -957735.74 1527671.52
  RVEL -1498.933 7331.026 -1778.090
  AROT 109.61 -8.53 80.06
  PRPLEVEL 0:1.000
  DOCKINFO 0:0,GL-01
  IDS 0:588 100 1:586 100 2:584 100 3:582 100 4:580 100
  NAVFREQ 0 0
  XPDR 466
END
Mir
  STATUS Orbiting Earth
  RPOS 3742224.30 336310.77 5500808.52
  RVEL -6398.637 264.848 4340.065
  AROT 0.00 -45.00 90.00
  IDS 0:540 100 1:542 100 2:544 100
  XPDR 482
END
Luna-OB1:Wheel
  STATUS Orbiting Moon
  RPOS -1532271.66 1630683.68 2507.86
  RVEL -1078.726 -1013.445 -0.514
  AROT 0.00 0.00 -168.19
  VROT 0.00 0.00 10.00
  IDS 0:560 100 1:564 100
  XPDR 494
END
GL-30:DeltaGliderIII
  STATUS Landed Earth
  POS -118.1606277 35.0558777
  HEADING 165.00
  RCSMODE 0
  PRPLEVEL 0:0.995 1:1.000 2:0.983
  NAVFREQ 94 524
  XPDR 0
  MeshSkin DeltaGliderIIIMining
  NOSECONE 0 0.0000
  GEAR 1 1.0000
  AIRLOCK 0 0.0000
  INNERDOOR 0 0.0000
  COCKPIT 0 0.0000
  PRADIATOR_PROC 0 0.0000
  StartPower_ext 0
  StartPower_batt 0
  StartPower_cell 0
  Apu_start 2
  Gen1 2
  Gen2 2
  GenSelector 1
  PowerHud 2
  PowerMfd 2
  PowerRadio 2
  PowerAirlock 2
  PowerEngine 2
  PowerLifepack 2
  PowerAp 2
  PowerMainBus 2
  PassengerSeat 1
  Strobe 1
  HydGearPress 2
  LevelBatt 100.0002
  Emergency_power 10000.0000
  Force_Canopy 0
  VoltageStartBus 0.0000
  VoltageGen1 96.2820
  VoltageGen2 96.2819
  VoltageGenBus 96.2820
  ExtFuelHatch 0
  ExtFuelValve 0
  DockFuelValve 0
  FuelInputSelector 0
  XFeedFuel 0
  DumpMainFuel 0
  DumpRcsFuel 0
  HoverValve 2
  MainValveL 2
  MainValveR 2
  RcsValve 2
  AirIntake 2
  TurboPump 0
  ComputerDisplay 3
  HudMode 0
  O2tankALevel 99.9681
  N2tankALevel 100.0000
  O2tankBLevel 100.0000
  N2tankBLevel 100.0000
  DockInputValve 0
  ExtInputValve 0
  InputSelector 0
  ButtonTankAO2 2
  ButtonTankAN2 1
  ButtonTankBO2 2
  ButtonTankBN2 1
  ButtonAFan 2
  ButtonAFilter 2
  ButtonACooling 2
  ButtonAMoist 2
  ButtonBFan 2
  ButtonBFilter 2
  ButtonBCooling 2
  ButtonBMoist 2
  Radiator 0
  ShipControl 5
  LifeDisplay 3
  CabinO2Level 21.3888
  CabinCO2Level 600.0000
  CabinTempLevel 21.2000
  CabinPressure 14.7000
  CabinMoistLevel 36.0000
  CabinDustLevel 0.0001
  CabinO2Setting 21.4000
  CabinTempSetting 21.2000
  CabinPressSetting 14.7000
  O2ConsumptionSetting 1
  PassengerNumber 4
  PilotName Cmdr_Jimmy_Dean
  PilotAge 29
  BasePilotPulse 60.0000
  Passenger1Name Jimmy_Griggs
  Passenger1Age 26
  Passenger1BasePulse 66.0000
  Passenger2Name Ryan_Simmons
  Passenger2Age 28
  Passenger2BasePulse 72.0000
  Passenger3Name Kelly_Putnam
  Passenger3Age 28
  Passenger3BasePulse 65.0000
  Passenger4Name Chris_Dambro
  Passenger4Age 29
  Passenger4BasePulse 72.0000
  FailGearFailure 0
  FailGearCollapse 0
  FailLeftMainEngine 0
  FailRightMainEngine 0
  FailHoverEngine 0
  FailRcs 0
  FailSurfaceControl 0
  FailComputer 0
  FailComputerBlueScreen 0
  FailAutopilot 0
  FailExtRadiator 0
  FailAirbrake 0
  FailNoseCone 0
  FailCanopy 0
END
END_SHIPS

----- SNIP -----

And the flight plan:

DeltagliderIII suborbital flight plan
KMHV-KTTS

Matt Weidner
matthewweidner@sbcglobal.net

1 Introduction

This document outlines a flight plan from Mojave
airport (KMHV) to NASA's Titusville, FL Shuttle Landing
Facility (KTTS).

You need to download and intall the Mojave Spaceport
base addon for Orbiter from AVSIM [http://library.avsim.net/download.php?DLID=54384] and the BaseSync MFD
from Jarmonik's Interplanetary MFD page [http://koti.mbnet.fi/jarmonik/BaseSyncMFD.zip]

2 Preflight

Loading the scenario file will place your
DeltagliderIII, GL-30, holding short of runway 30 at
Mojave airport.

2.1 BaseSync MFD v2.0

Configure the BaseSync MFD as your primary guidance instrument.

1. TGT: Cape Canaveral

2. E/D: Direct

3. MOD: Press MOD button until MFD displays text only

4. ENC: Closest Passage

5. NUM: 1

2.2 COM/NAV receiver stack

Tune the NAV radios to use the HSI MFD to track your
inbound course to KTTS.

1. NAV1: 112.70 - initially this tunes the HEC VOR, but
  when arriving it will track the KSC VOR.

2. NAV2: 134.20 - shuttle landing facility ILS.

2.3 HSI MFD

Configure the HSI MFD to track your inbound course to KTTS.

1. Left HSI indicator slaved to NAV2

2. Right HSI indicator slaved to NAV1

3. Rotate right HSI OBS indicator to course 136

2.4 MAP MFD

Configure the MAP MFD to track your course.

1. TGT: Cape Canaveral

2. TRK: ON

3. ZM: ON

2.5 Flight controls

Configure the crafts flight controls.

1. Turn Ship Ctrl dial to ATM AUTO

2. Apply full UP elevator trim so the trim indicator is
  located at the bottom of the gauge.

3. Left MFD: SURFACE, GSP velocity

4. Right MFD: BASESYNC

5. FC BACKUP Display to REENTRY mode (D3)

3 Ascent/Descent

Takeoff from runway 30.

1. At wheels up, turn right (20-30 bank) until RInc on
  Basesync MFD indicates 0.14. Simultaneously begin a
  100-120 m/s climb to 52km.

2. Maintain 0.14 RInc until TAEM maneuvers. We will be
  arriving at KTTS from the northwest.

3. MECO @ GSP VEL: >4.0 km/s <4.010 km/s ALT: 52km

4. Descend and maintain 50km Vspd: -20m/s

5. At BaseSync MFD DST: 2.35M, begin -25 m/s descent.

6. Monitor hull temperature on FC BACKUP display.

7. Around ALT: 45km, sufficient DYN PRESS will be
  present to adjust pitch with elevator trim. Increase
  descent rate to -30 m/s

8. At BaseSync MFD DST: < 500km (ALT <= 35km) switch
  RIGHT MFD to HSI. Verify LEFT HSI NAV2, RIGHT HSI
  NAV1 & OBS CRS 136.

9. Begin TAEM maneuvers.

3.1 TAEM maneuvers

+---------------+-----------+-----------+---------------------+-------+------------------+
| BaseSync DST  | Altitude  |   VSpd    |      Velocity       | Mach  |   Instructions   |
+---------------+-----------+-----------+---------------------+-------+------------------+
|    400 km     |  33 km    | -30 m/s   |         --          |  --   | VSpd to -50 m/s  |
+---------------+-----------+-----------+---------------------+-------+------------------+
|    230 km     |  28 km    | -50 m/s   | 1.3 km/s HUD (GSP)  |  --   | Turn left to 110 |
+---------------+-----------+-----------+---------------------+-------+------------------+
|    129 km     |  23 km    | -50 m/s   | 940 m/s HUD (GSP)   | 3.2   | VSpd to -120 m/s |
+---------------+-----------+-----------+---------------------+-------+------------------+
|    80 km      |  18 km    | -120 m/s  |      360 IAS        | 2.3   |                  |
+---------------+-----------+-----------+---------------------+-------+------------------+
   

Descent profile

1. Surface MFD to IAS VELOCITY.

2. On KSC VOR radial passage (RIGHT HSI), report runway
  in sight (pilot's 1:00-2:00). Turn right to begin
  runway alignment maneuver. Follow the ILS localizer,
  disregard glideslope indicator. Put the "meatball"
  velocity vector indicator on the runway.

3. Before deploying airbrake to regulate velocity,
  check DYN PRESSURE < 45 kPa. Deploying the airbrake
  will cause the glider to "nose down".

Now, put that bird on the runway!!

------- EOF -------

Argh!  The PDF looks MUCH nicer.  I'll go ahead and email the PDF to you.  If you can reproduce the suborbital flight then I
might upload the PDF to Orbithangar.  Let me know what you think or if any calrifications are needed.

Enjoy!

[StarLost]

JimmyDean, you are my friend.  I'm enjoying a four day weekend, this weekend (Canada's July 1st National fete), so I'll give
her a shot (in between watching Deep Impact's approach).

I'd love a copy of the PDF. Please email to one of these addresses:

starlost@inorbit.com
imstarlost@yahoo.ca
kecarter@execulink.com

And real life intruding ... ? My boy, you have no idea. My last six months have been the experience from hell.  Good thing
for friends like Doc Holiday and sidereal.

Just keep it straight and fly right !!

[StarLost]

Just in case the email gets screwed up, all items were received and in good order. I'm looking forward to trying them out.

Thanks again.

Kenny

[JimmyDean]

Hi ya Starlost!

I got your email.  Good luck on your flight!

[laserpithium]

Hi every one,

I'm  currently working on a MFD for ballistic trajectories.
But it will only work for planets without atmosphere (as the Moon), the equations become horrible when I tried to take into
account atmosphere action.
I've just finished to calculate the good equations, release I don't kown when... I'm afraid more than one month...

[Simonpro]

Isn't the easiest way to do this to use the equations of motion? That way you can include as many purturbations as
you wish and not have to bother about the messiness of the equations. Only downside is the need for a funky
integrator routine, but there are a great many of those available on line - using the equivalent to that in Orbiter (RK4)
would be a good start

[laserpithium]

Simonpro wrote:
Isn't the easiest way to do this to use the equations of motion? That way you can include as many purturbations as
you wish and not have to bother about the messiness of the equations. Only downside is the need for a funky
integrator routine, but there are a great many of those available on line - using the equivalent to that in Orbiter (RK4)
would be a good start

I'm not used to the Orbiter SDK, I just begin !  
So you think that RK4 will not take too much time ? It's possible to use it without having 5 minutes of calculus ?

[Simonpro]

If you can wait until the weekend I'll post some code here that might do the job, it's on my computer back
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