In order to make this easy to understand I will use some words as variables.  When I talk about “water” I am initially talking about h2o water, but later I will change to other forms of reaction mass but still use the term “water” with “” to clearly tie the reaction mass back to the initial easy to understand example.

Do you believe it is possible to have a solar powered boat on a lake on Earth?

It is and you can purchase one here:

https://www.dasolar.com/solar-energy/solar-powered-boats

Do you believe it would be physically possible for this solar powered boat to occasionally fill a internal tank with water and then using a “jet boat” motor to expels it at 900 km/hr?

Assuming the water exhaust remained water and didn’t evaporate or leak out the bottom of the lake do you believe that the lake would never run out of water?

If the boat is solar powered and never runs out of sunlight and the lake never runs out of water the Delta-V or Delta velocity will be set by the boat lifetime.  This is because when the tank is empty there is water in the lake to refill it.  Each segment from internal tank full to internal tank empty is identical and no fuel is carried between these segments.  This is a simple but important concept we need to focus on for a second.

Why is the water always in the lake?  Because Gravity pulls it to the lowest point which is always in the lake as the shore is higher.

The boat can function forever only because gravity is repositioning the water.  The boat can function well because it does not carry reaction mass between stages so that each segment adds (2 segments mean you fill the internal tank for segment 1 and then fill it the same amount with segment 2 if you had N segments the total would be 1+1+1+1………=N internal tanks worth of water).  Mass fraction is equal to the fuel used + the mass of the boat divided by the mass of the boat so when comparing the fuel used in terms of mass fraction we need to subtract out the mass of the boat before we multiply and then add it in again at the end.  So the mass fraction for N segments has a N_Mass_Fraction= N*(Segment_Mass Fraction -1) +1  .

Now we will transition to talking about space.

A spacecraft called the “pusher” will replace the “jet boat”.  Currently rockets perform this role.  They expel their “water” (rocket fuel) at much higher than 900 km/hr but they never refill their internal tank.  Worse still when rockets expel their “water” (jet fuel) in space they disburse it so that it can never be recovered unlike the example above the world will eventually run out of rocket fuel “water” .  Because they never refill the rocket fuel “water” tank  they have to carry fuel for future segments in the early segments which means their mass fractions multiply not add.  This can be verified by using a rocket equation solver N_Mass_fraction= Segment_Mass_Fraction^N which is much much larger than when you can add segments.  Put in 453 s Isp and step up from 1000m/s to 2000m/s to 4000m/s to 8000m/s to 16000m/s you can clearly see the mass fraction squares as the distance doubles.

I use this rocket equation solver but any will do:

http://www.quantumg.net/rocketeq.html

Returning to the “pusher” a simple change allows us to achieve the benefits of the “jet boat” model on Earth.  Instead of burning the fuel for the highest Isp this “pusher” uses 8Gs of acceleration over a track of 400m using Maglev as the acceleration.  If you believe 8Gs is unattainable substitute the number you believe and keep following the outcome doesn’t change much with lower Gs acceleration.  Now that lower acceleration is being used, complex structures can survive the expulsion and instead of jet fuel “water” we can use as “water” a mass which I will call a “brick”.  The “brick” has mass so like water or jet fuel it also provides momentum to the “pusher”.

The key is that the “brick” is itself a solar sail powered spacecraft.  Once it is launched from the “pusher” it can use the sun’s photons and its ability to navigate to perform the role of gravity in the jet boat example.  The “bricks” can navigate from where a “pusher” expels them to reach the location and velocity where they will intercept at VERY low relative velocity (less than 5km/hr difference) the next “pusher” .  “Bricks” are only used once per transit so the speed that the “brick” accelerates doesn’t influence the acceleration of the “pusher”.

The “pusher” has 10% by mass solar cells with a energy density of 300 Watts/kg.  This provides it with 30 W/kg average over the entire spacecraft.  If the internal “tank” carries 50% the mass of the “pusher” spacecraft then the joules to eject the entire “tank” of “bricks” will be joules=1/2 M 250m/s)^2 and we have already stated that the mass of the fuel is 50% the mass of the “pusher” so moving 1 kg worth of “pusher” will be joules =(1/2)(1/2 kg)(250m/s)^2=15,625 joules and the solar cell panels can source this energy at 30 Watts/kg so each “tank” will take 520.833 seconds.  In this 521 seconds the “pusher” has increased by 100 m/s because the 250m/s is 25.5s Isp and the rocket equation gives us 101 m/s of delta V for a mass fraction of 1.5 of 25.5s Isp fuel.  So delta V is 100m/s and the time to achieve it is 521 seconds and we can solve for Acceleration =Velocity change/time which would be 191 mm/s^2.  But this assumes 100% transfer from electrical energy to kinetic energy which is far too optimistic so let assume 10% of the energy is transferred to kinetic energy which should be far too pessimistic and I claim that the acceleration is >19 mm/s^2.  This is important because this level of acceleration can compete with rocket fuel for interplanetary transit durations (other efficient forms of thrust take much longer because they have much lower acceleration).

The “brick” can be reused over its lifetime.  In some situations such as rotating the Earth this reuse should occur every 3-6 months for the duration of a 30 year lifetime giving 60-120 uses each of which is part of a segment that transfers 100 m/s to the “pusher” thus giving an effective 6km/s  –  12km/s of delta V for a Earth sourced mass fraction of 1.5.  This translates to an average Isp of 1509s – 3019s.  In other locations the reuse could be as low as 5 times in the 30 year life with each “brick” taking as much as 6 years to reach the next “pusher” location.  NASA’s best Isp for a rocket is 453s Isp and all ion propulsion techniques that have more than 1500s Isp are MUCH lower acceleration and not suitable for fast transits.

The primary benefit is that each segment adds rather than multiplies its mass fraction when building a larger transit.  This allows transits that seem economically impossible now such as a 80km/s one way transit to Mars leaving outside the hohman transfer window.  Currently this would require a round trip mass fraction of 4491245393957829.5 but with 6 times reuse within a 30 year lifetime and 99% recycling of “brick” mass to remanufacture a 2nd generation “brick” the average mass fraction for this round trip transit could be brought down to a mass fraction of 2.4.

You can verify the math :

Round trip mass fraction is 1+1600* (100m/s) segments of 0.5 mass each=801 mass fraction

6 Round trips for one set of “bricks” is 1+800/6= 134.33

600 round trips for one set of lifetime recycled bricks is 1+800/600=2.4

Fuel used (4491245393957829.5  –  1)/(2.4  -1)=3.2 E15

This is 3,200,000,000,000,000 times better than 453s Isp can do the same trajectory.

Transferred Momentum

Simple physics.  Honest calculations. Amazing results.

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