That low-mass design is really neat, and I'm sure you could shave off a little mass. Are we considering returning from the moon as well as landing?
I would also draw your attention to a form posted a while ago,
diving into the math of SSTO spacecraft.
In this, I found that the best engine for SSTO spacecraft is the broadsword because of their twr. However, if you are designing stages meant to fly in space and which do not need a specific twr, the frontier engine should be considered for any spacecraft pushing a payload of more than 150 tonnes. That is, (payload of 150)||(stage fuel, ~225)(Frontier engine)<. (P)||(F)<. As such, broadsword engines are not always the best, but they are for most SSTO applications (Unless you're going for part count).
I'll try my hand at the math.
Using
Altaïr's incredible
DeltaV map, and
this map, ground>LEO is 2800, LEO> LLO is (640+59+122) OR (650+140) (821 OR 790. Call it 800.) LLO>ground is 464 (call it 500). When returning, we need to go to LLO, then intersect earth, but use an aerobreak. Thus, we need dv=2800+800+500*2+(800-640)=4760 (with return) or
dv=2800+800+500=4100 (without return)
And after the math comes the engineering. After all, who needs landing legs, right? You can always try to cut corners, which works so well in aerospace.
Let's assume the design is 4 things- probe, parachute, fuel tanks, and engines.
Payload is then probe+parachute=2.5+.5=3.0 tonnes.
deltav=isp*g*ln(M0/Mfin) //Mass final over mass at t0
deltav/(isp*g)=ln(M0/Mfin)
M0/Mfin=e^(deltav/(isp*g))
Mfin=M0-Mfuel*.9 //Final mass is initial minus reaction mass. Mfuel is wet mass of fuel tanks
M0=Mp+Me+Mfuel // Mp= Payload = 3, Me=Engine mass
My=Mp+Me // Payload and engines can be lumped together. Y not?
Mfin=My+Mfuel*.1
R=e^(deltav/(isp*g)) // Just to simplify writing it, since this term will not be broken up
(My+Mfuel)/(My+Mfuel*.1)=R
(My+Mfuel)=R*(My+Mfuel*.1)
My+Mfuel=R*My+R*Mfuel*.1
Mfuel-R*Mfuel*.1=R*My-My
Mfuel*(1-R*.1)=My(R-1)
Mfuel=My(R-1)/(1-R*.1) // Basically this says that the fuel required is the mass of the payload and engine times a ratio
Ok, for one-way, using broadswords. I will assume broadswords are best for this case.
e^(4100/(9.8*281))=R=4.432.
My=3+2.5*Ne // Ne is the number of engines. Assume 2
My=3+2.5*2 = 8 tonnes
Mfuel=8*(4.432-1)/(1-4.432*.1)=49.310 tonnes. Round to 50 tonnes
M0=58 tonnes initial mass.
TWR=Ne*T/M0=2*40/58=1.38 which is perfect
Assuming 4000 dv, that works out to 45.74 tonnes fuel. Make it 46 tonnes, overall mass is 54 tonnes, twr is similar. That's basically what
Horus Lupercal found.
Using Frontier?
e^(4100/(9.8*285))=R=4.340.
My=3+8*Ne // Ne is the number of engines. Assume 1
My=3+8*1 = 11 tonnes
Mfuel=11*(4.340-1)/(1-4.340*.1)=64.90 tonnes. Round to 65 tonnes
M0=65+11=76 tonnes initial mass.
TWR=Ne*T/M0=1*112/76=1.47 which is in the same ballpark.
Result? The mass of a frontier makes a world of difference, in a negative manner.
Ok, what about for a return trip, 4800 delta-v, using broadsword engines.
10 engines, fuel is 308 tonnes.
M0 is 336 tonnes
TWR is 1.19, which is absolutely minimally marginal at best. A low TWR also means more deltav is wasted on takeoff.
I'm a bit rushed to finish this up, but as you can see, just going from 4100 to 4800 deltav is a massive increase in mass. This is why it's so important to stage, of course.
I hope this helps.