How to use T/W when designing a lander?

[Dave Kerbin]

I'm gearing up for a mission to Duna. I've already sent an ion powered probe to learn about interplanetary travel and to engage in a long term observation mission in orbit of Duna and Ike.

Now I want to do a manned mission but it's going to be in two parts. The first part is sending 'pathfinder', an advanced unmanned mission designed to accomplish a number of goals:

1. Test aerobreaking on Duna approach.

2. Establish a fuel depot at Duna to support a future manned mission.

3. Drop up 6 to surface probes to scout a good landing site.

4. Delivery and perform a test of the Duna lander under automatic control.

I've assembled most of pathfinder already. The probes are the little bits on the left. The fuel to get to Duna is stored in the dropaway tanks that I've brought up and docked to the 'tail' of the ship.

What is missing is the Duna lander that will go on the nose docking port.

I'd like to reuse my standard manned ascent craft as it would be in the spirit of my space program. It has a Delta-V of over 2000 m/s, so by the cheat sheet it would seem like I can add extra parachutes to keep it in one piece, a ladder and some landing gear to set down with most of the fuel left, then take off again as a SSTO ship.

My biggest concern is thrust to weight, since without some math I have no guarentee the ship will be able to take off. The formula seems to suggest that I would take the engine's thrust in kN and divide it by the spacecraft's mass multiplied by the local gravity. So if the craft weighs 17t, gravity is 2.94 m/s2 and thrust is 220 then I get a value of 4.4...and I don't know if that is good or not.

Do I have the math right for calculating T/W?

What is a good T/W ratio for getting a craft off Duna? (overcoming gravity and the atmosphere). I assume it must be greater then 1 or it wouldn't leave the ground.

Have I made a terrible mistake with Delta V for my lander? (Mk1-2 + X200-16 + Poodle can get into orbit with fuel to spare)

Edited September 29, 2013 by Dave Kerbin

[Guest]

You'll need a planet-relative TWR > 1 in order to reach orbit.

Two parachutes on that craft should help save some delta-V on the way down and the cheat sheet is pretty close. 2km/s should be enough to land and return but you might want to bring extra for rendezvous. Or do that with the carrier, whatever. Just keep in mind all the things you'll be doing when figuring out your delta-V budget.

Edited September 29, 2013 by regex

[Specialist290]

Taking this item-by-item:

Do I have the math right for calculating T/W?

Yes, you do.

To put it in layman's terms: Your thrust-to-weight ratio is the measure of the amount of force exerted by your engines pushing up versus the force exerted on the craft by gravity trying to pull it down. If it's over 1, that means your engines are enough to overcome the planet's gravity; under 1 means You Will Not Go (Back) To Space Today.

The number the equation puts out is the number of units of force the engines put out for every unit of force generated by gravity. While engine thrust can be measured directly, surface gravity is a measure of acceleration, and to get a meaningful value for force we have to plug that figure into the equation "F = ma" along with the craft's mass.

What is a good T/W ratio for getting a craft off Duna? (overcoming gravity and the atmosphere). I assume it must be greater then 1 or it wouldn't leave the ground.

As I explained above, that is indeed correct. I don't have a hard-and-fast answer for which specific TWR would be ideal, but the KSP wiki page for Duna should have some helpful info, including a terminal velocity chart to help guide your ascent.

Have I made a terrible mistake with Delta V for my lander? (Mk1-2 + X200-16 + Poodle can get into orbit with fuel to spare)

Give me a second to verify the math myself. I'll edit it into this post when I'm done.

EDIT: Calculating from the three parts you've given (and not including the other "greebles" on the craft, which will bring the mass ratio down a little by virtue of adding extra mass), I get a full mass of 15.5 and a dry mass of 7.5. A "Poodle" provides a vacuum Isp of 390. Plugging these in to the rocket equation, we get:

dv = 9.81m/s^2 * 390s *ln(15.5 / 7.5)

dv = ~2775m/s

This should be more than enough to land and take off again, especially if you help along the process with parachutes.

EDIT2: Because it's late, I'm bored, and it caught my fancy, I figured I'd do a practical exercise. I'm sharing it since you might find it helpful.

Most of the delta-v charts I've referenced tell me it takes about 1380m/s of delta-v for a one-way trip to or from Duna. For the sake of convenience, let's include a little "elbow room" and say you want a lander with 1600 m/s delta-v.

We can plug that value into the rocket equation along with the Isp value for the Poodle and standard gravity (constant):

1600m/s = 9.81m/s^2 * 390s * ln(m0 / m1)

Solving for our mass ratio, this gives us:

(m0 / m1) = e^(1600m/s / 9.81m/s^2 * 390s)

(m0 / m1) = ~1.52 (with some judicious rounding)

Inverting the ratio gives us the payload fraction:

1 / 1.52 = ~0.658 = 65.8% payload

And subtracting this from 1 gives us the propellant fraction:

1 - 0.658 = 0.342 = 34.2% propellant

We know that an X200-16 fuel tank holds 8 tonnes of fuel (Full mass 9 - Dry mass 1 = 8), so we can put this in terms of a ratio to get the total mass of the craft for our target delta-v:

0.342 = 8t / x

0.342x = 8t

x = 23.4 tonnes

Subtracting the known propellant mass of 8 tonnes gives us the dry mass of the craft:

23.4t - 8t = 15.4 tonnes

As a check, we can plug all this back into the delta-v equation, and it should come out with something close to what we started with:

dv = 9.81m/s^2 * 390s * ln(23.4t / 15.4t)

dv = ~1601m/s

And for an extra check, we can divide dry mass by full mass to get the payload fraction again:

15.4t / 23.4t = ~0.658 = 65.8% payload

In other words, once we take into account the weight of the Poodle, the command pod, and the dry mass of the fuel tank, we can find how much mass we have to spare for "extra goodies" for the mission (such as parachutes, landing legs, docking ports, RCS tanks and thrusters, decouplers, etc.):

15.4t - (4t + 1t + 2.5t) = 7.9 tonnes

Pretty nifty, isn't it?

Edited September 29, 2013 by Specialist290

[Camacha]

Let me just make sure I am able to find this topic a little later on.