need help testing 10m heat shield over Duna at 2450-2850 m/s!

[jasonlee]

went to duna with a probe for the first time ever, but could NOT get an orbit large enough to give me a max velocity of 2450-2850 m/s between 28K and 44K over duna in order to test this heat shield for a lucrative contract. I ain't giving this advance back! So, I need to complete this mission, lol. I'm gonna be dogged about it.

Any suggestions here? Sorry if it's been asked but I couldn't find the answer myself and I've tried to the point of frustration already. Thanks in advance, folks!

 

EDIT: In thinking about this, would getting into a solar orbit first be the way to go, then simply crash from that large orbit into Duna atmo? Or will it have to be some sort of powered entry?

Edited June 24, 2019 by jasonlee
additional info

[steuben]

Don't orbit... well the orbit isn't going to be your primary goal. Just a means to an ends. I haven't done this kind of contract from orbit, usually from the surface.

But, my back of the envelope mission profile would be:
1. get into a nice orbit, a nice sub-Ike one.
2. lower periapsis to about the mid point of the altitude bracket. in this case about 35km
3. burn to raise speed and keep periapsis constant
3.a if you get up to speed and are not in the altitude bracket, reduce the throttle to maintain speed. Don't forget to change to surface vs orbit speed.
4. if you are not in the speed bracket, Burn _hard_ when you are in altitude bracket.

(Note: getting to Duna is left as an exercise for the reader.) You'll want to use LFO for this rather than NERVs or Dawns. Then once complete either watch the fireworks or slowdown for recovery.

 

[jasonlee]

3 minutes ago, steuben said:

Don't orbit... well the orbit isn't going to be your primary goal. Just a means to an ends. I haven't done this kind of contract from orbit, usually from the surface.

But, my back of the envelope mission profile would be:
1. get into a nice orbit, a nice sub-Ike one.
2. lower periapsis to about the mid point of the altitude bracket. in this case about 35km
3. burn to raise speed and keep periapsis constant
3.a if you get up to speed and are not in the altitude bracket, reduce the throttle to maintain speed. Don't forget to change to surface vs orbit speed.
4. if you are not in the speed bracket, Burn _hard_ when you are in altitude bracket.

(Note: getting to Duna is left as an exercise for the reader.) You'll want to use LFO for this rather than NERVs or Dawns. Then once complete either watch the fireworks or slowdown for recovery.

 

thanks Steuben. Getting to Duna isn't a problem, just getting up to that speed. Will try your strategy. Thank you!

11 minutes ago, steuben said:

Don't orbit... well the orbit isn't going to be your primary goal. Just a means to an ends. I haven't done this kind of contract from orbit, usually from the surface.

But, my back of the envelope mission profile would be:
1. get into a nice orbit, a nice sub-Ike one.
2. lower periapsis to about the mid point of the altitude bracket. in this case about 35km
3. burn to raise speed and keep periapsis constant
3.a if you get up to speed and are not in the altitude bracket, reduce the throttle to maintain speed. Don't forget to change to surface vs orbit speed.
4. if you are not in the speed bracket, Burn _hard_ when you are in altitude bracket.

(Note: getting to Duna is left as an exercise for the reader.) You'll want to use LFO for this rather than NERVs or Dawns. Then once complete either watch the fireworks or slowdown for recovery.

 

Another ? for you Steuben: do you think a Terrier will have enough thrust to reach those kinds of speeds or do I need something like a Poodle or other larger vacuum optimized engine?

[steuben]

It depends on your total payload mass, and what speed you get at the bottom of your orbit. You are after TWR here, rather than efficient burns.  It should probably work with either. The poodle gives ~10TWR, with 2.2 km/s dv, and the terrier ~2.8 TWR with 2.8 km/s dv. When strapped to the bottom of the 10 m shield and a X200-8.

[Foxster]

Wouldn't coming in from Dres get up a fair head of steam?

[Zhetaan]

On ‎6‎/‎24‎/‎2019 at 8:21 AM, jasonlee said:

went to duna with a probe for the first time ever, but could NOT get an orbit large enough to give me a max velocity of 2450-2850 m/s between 28K and 44K over duna in order to test this heat shield for a lucrative contract. I ain't giving this advance back! So, I need to complete this mission, lol. I'm gonna be dogged about it.

This can be calculated, so let's do that.

Objects in circular orbits orbit at a constant speed; the more elliptical the orbit, the more the speed varies between the apoapsis and periapsis.  Lower orbits are also faster orbits, so to get the most from a gravitational dive to Duna, let's assume that you want the 28,000 metre limit as your periapsis, and since we want a value that will complete the contract, let's use the minimum velocity of 2,450 m/s.

First, we need something called the vis-viva equation:

v² = μ [(2 / r) - (1 / a)]

Where:

v is the relative velocity,
μ is the standard gravitational parameter (for Duna, this is 3.0136321 x 10¹¹ m³/s²),
r is the radial distance from the centre of mass (KSP measures surface altitudes, not radial altitudes, so we need to add 320,000 metres to the altitude for this value), and
a is the semi-major axis of the orbit, also measured according to radial distance from the centre of mass.

For our purposes, we know the radial distance we want to use (28,000 + 320,000 = 348,000 metres) and the velocity (2,450 m/s), so we can solve for the semi-major axis.  With a bit of algebra, we get this:

a = 1 / [(2 / r) - (v² / μ)]
a = 1 / [(2 / [348,000]) - ([2,450]² / [3.0136321 x 10¹¹])]
a = 1 / ([5.74712643 x 10^-6] - [6.0026 x 10⁶ / (3.0136321 x 10¹¹)])
a = 1 / ([5.74712643 x 10^-6] - [1.991782607 x 10^-5])
a = 1 / -1.417069964 x 10^-5
a = -70568.14 m

What happened?  How do we get a negative semi-major axis?

Put simply, we're looking at the wrong kind of orbit.  Even though the semi-major axis represents a real value when dealing with elliptical orbits, there are other kinds of orbit; in this case, a negative semi-major axis means that we're dealing with a hyperbolic orbit.  In other words, the contract is specifically asking you to test this heat shield on an interplanetary insertion.  (Technically, the negative semi-major axis is a real value, too; it measures the distance from the periapsis to the point where the hyperbolic asymptotes cross--but since that direction is opposite the centre of the primary, the value is negative--and if you don't know what those terms mean, that's okay.)

Even so, I can still help you.  Hyperbolic orbits have a particular parameter called the hyperbolic excess velocity, which is a measure of how much faster than escape velocity an object on such an orbit moves.  This value is often termed v_inf or v_∞ in the equations.  It's also easy to calculate when you already have the semi-major axis:

v_∞ = √(-μ / a)

v_∞ = √[-(3.0136321 x 10¹¹) / (-70568.14)]
v_∞ = √(4270527.89)
v_∞ = 2066.53 m/s

There is an inaccuracy involved because Duna's sphere of influence begins a bit inside the effective infinite distance (just a little bit) but it isn't extremely large.  The point is that if you enter Duna's sphere of influence with approximately 2067 m/s relative velocity on a trajectory that aims for a 28 km periapsis, then you should touch the minimum required velocity for your contract.  Obviously, more velocity would be a good idea in this case:  you have to account for error, aerobraking (not much but it's there), and the fact that I just calculated the essential minimum velocity to just barely complete the contract; you'll likely want a margin anyway.

Or you could, as others have suggested, simulate such a trajectory by the use of a massive rocket pointed down.  This is one problem where more boosters will actually help.

Alternatively, there is nothing saying that you have to aim for a periapsis at 28 km; the contract only requires you to have the right velocity at that altitude.  You could always try to ram the core of the planet and see whether you reach the required velocity in that case.  KSP is versatile; whether you want to make peaceful exploration of the skies or knock those pesky planets out of the way, it has something for you.

Edited June 28, 2019 by Zhetaan

[AHHans]

54 minutes ago, Zhetaan said:

whether you want to make peaceful exploration of the skies or knock those pesky planets out of the way, it has something for you.

And with the passive seismometer from the Breaking Ground DLC you can have both.

[jasonlee]

Zheetan, that is some respectable work. As a scientist myself (not a physicist, unfortunately), I LOVE the work you took the time to demonstrate. 

Between you and Steuben, I think I will try this again this weekend. Thank you both!