View Single Post
  #6  
Old April 11th 17, 04:49 AM posted to sci.space.policy
William Mook[_2_]
external usenet poster
 
Posts: 3,840
Default Reusable Laser Launcher

On Tuesday, April 11, 2017 at 3:46:44 PM UTC+12, William Mook wrote:
On Tuesday, April 11, 2017 at 9:38:05 AM UTC+12, Serg io wrote:
On 4/10/2017 4:14 PM, Robert Clark wrote:
The U.S. military is making progress in high power lasers. The Navy
expects to field a ship-born 150 kW laser:

US Navy Prepares To Fire 150-Kilowatt Laser Gun From Sea Vessels.
https://www.youtube.com/watch?v=5fr0SM8vNk8

And the Army expects to field a laser carried by trucks at 60 kW power:

US Army gets world record-setting 60-kW laser | Latest News Updates Today.
https://www.youtube.com/watch?v=L9AC1njoP5o

Assuming linear scaling,


not linear at all, dude !


What makes this nonlinear potentially, is the ability to use air, and lower the exhaust speeds to get more thrust for a given amount of power.

Energy = 0.5 * mass * velocity^2

and

Force = mass * acceleration.

Now,

acceleration = derivative( velocity )

so;

Force = mass * derivative( velocity )

then also

Force = derivative( mass ) * velocity

finally

Power = derivative( energy )

so
Power = derivative( mass ) * velocity^2

Knowing that;

derivative( mass ) = mass flow rate

And being limited to 50 MW of power in a purely rocket based system, since it takes an ideal delta vee of 9.2 km/sec to achieve low earth orbit (7.9 km/sec speed, 1.3 km/sec loss due to air drag and gravity) the most material is projected to orbit at this power setting by setting the exhaust speed to delta vee. Making it higher, means you waste energy by putting too much in the exhaust jet. Making it lower means you waste energy lifting more propellant than you need.

Now, air around the vehicle, changes that calculus.

We can start at very low exhaust speeds using air as a propellant, and get very large thrusts at lift off, whilst using the propellant at the same power settings, to produce less thrust, at altitude with higher exhaust speeds.

Ve (m/sec) mdot (kg/sec) F (Newtons) kgf Pounds (force) GLOW (pounds)
9200 1.181 10869.565 1108.387 2438.452 1741.751
9000 1.235 11111.111 1133.018 2492.640 1780.457
8000 1.563 12500.000 1274.645 2804.220 2003.014
7000 2.041 14285.714 1456.737 3204.822 2289.159
6000 2.778 16666.667 1699.527 3738.959 2670.685
5000 4.000 20000.000 2039.432 4486.751 3204.822
4000 6.250 25000.000 2549.291 5608.439 4006.028
3000 11.111 33333.333 3399.054 7477.919 5341.371
2000 25.000 50000.000 5098.581 11216.878 8012.056
1000 100.000 100000.000 10197.162 22433.757 16024.112

Limiting the exhaust speed from heated air to 12x sound speed, and limiting the use of air as propellant to speeds lower than 12x sound speed means that we can lift a 4,000 pound vehicle off the ground, and accelerate it to 4,000 m/sec. This reduces the delta vee of the rocket portion to 5,200 m/sec, and when the propellant is used, it's exhaust is heated to the point where it produces 3,500 pounds of force - with an exhaust speed of 5,200 m/sec. Or 0.875 gee. Which means if the flight angle is pitched 61 degrees or less above the horizon, we can maintain or gain altitude, as we accelerate tangential to the ground.

Here we have 2,528.5 pounds of water, 500 pounds structure, 971.5 pounds of payload (over twice the weight to orbit! With the same power - using air at the outset)

We cut the size of the power plant in half, for the larger system, and reduce overall costs by the same factor.

The cost per pound on orbit is also cut in half - about $1.52 per pound.

The value remains the same.


A more detailed analysis uses calculus of variation and the aerodynamic and gravity losses involved at each moment of the flight, optimising exhaust speed to get the most out of the limited power laser, doing this increases the weight to orbit to, 1,374 pounds - by increasing the launcher size by this factor - and reducing exhaust speeds at launch accordingly.