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Old October 28th 17, 11:36 PM posted to sci.space.policy
William Mook[_2_]
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Default SpaceX BFR tanker as an SSTO.

You can buy them and do anything you can get a license to do. So, have at it!

With a 3.2 km/sec exhaust speed and the requirement to boost through a 9.2 km/sec delta vee to attain a 7.91 km/sec orbital speed (with 1.29 km/sec lost due to air drag and gravity losses) we have a propellant fraction of;

u = 1 - 1 / exp(9.2/3.2) = 0.943583860496223 ~ 94.36%

So, with a 3.5% structure fraction you could place 2.14% into LEO.

With a TSTO-RLV and the same structure fraction, dividing the delta vee by 2 to make each stage 4.6 km/sec we have;

u = 1 - 1 / exp(4.6/3.2) = 0.762479180904542 ~ 76.25%

So with a 3.5% structure fraction you could push 20.25% of each stage through 4.6 km/sec.

So, here you have 0.202520819095458 squared which is 0.0410146821670953 ~ 4.1%

Nearly double the take off weight into orbit.

Let's do three stages! 9.2 km/sec / 3 = 3.067 so,

u = 1 - 1 / exp(3.067/3.2) = 0.616468427123689 ~ 61.65%

So with a 3.5% structure fraction you have 0.348531572876311 ~ 34.85% payload on each stage.

0.348531572876311 cubed is 4.23%

A slight, but measureable improvement.

So, you can see there is a significant benefit to two stages over one.

Now, if your structure fraction is higher, the benefit of staging is higher. If we go from 3.5% to 5.0% structure fraction, we have

1 stage to orbit -0.64% - 155.85 t per t on orbit
2 stage to orbit - 3.51% - 28.44 t per t on orbit
3 stage to orbit - 3.71% - 26.96 t per t on orbit


On Sunday, October 29, 2017 at 3:44:43 AM UTC+13, Robert Clark wrote:

With VTOL using rockets, and with an advanced 'active' landing platform, no
landing gear is needed. Merely hold down clamps.

Catching Balls with Robots

https://www.youtube.com/watch?v=R6pPwP3s7s4

Which I discussed here;

Active Landing Pads - catch rockets

https://vimeo.com/37102557

BFR Mass Budget:

BFR system consists of 85 t second stage with 1,250 t propellant capacity -
delivering 150 t propellant for transfer to a BFR spaceship - after burning
1,100 t. 8 flights of a freighter refill the 1,200 t capacity BFR
spaceship.

85 t / 1250 t = 6.8% structure fraction.

Way more than needed.

We have 9.75 t of propellant to bring the 85 t structure to a soft landing
from 0.34 km/sec terminal velocity.

10% of the 95 t structure + propellant is 9.5 t - set that aside for
landing gear.

Tank fraction is 3.5% of the original capacity - 43.75 t.

7 Raptor engines at 1 t each is 7 t. That's 50.75 t sub-total. 9.5 t
landing gear 60.25 t sub-total.

Add 9.75 t propellant - and that's 70.00 t.

Add 15 t thermal protection and other hardware - and consumables - and you
have your 85.00 t budget.



Keep in mind there is a difference between the tanker and the spaceship
versions of the upper stage. The spaceship version has higher dry mass
because it has the passenger quarters and supplies for a 6 month trip to
Mars carrying 100 colonists. Since the tanker version doesn't carry this
passenger compartment it has much lighter dry mass. This is illustrated by
the ITS upper stage introduced last year:

https://i.imgur.com/GsyREf7.png

The ITS spaceship had a dry mass of 150 tons, and the ITS tanker a dry mass
of 90 tons.
The half-size BFR spaceship has a dry mass of 85 tons. Then applying similar
scaling to the BFR tanker we can estimate its dry mass as 50 tons.

It is the BFR tanker that would be used to deliver payload to LEO.

Bob Clark