### QED-ARC Engine ISP figures

Posted:

**Fri Sep 18, 2009 5:46 pm**Hello all,

i'm in the process of developing an addon for Orbiter, the free spaceflight-simulator. (http://www.orbitersim.com)

What i want to do is a SSTO spaceplane using Polywell reactors, inspired by the design proposed by Dr. Bussard for example in this paper:

http://www.askmar.com/Fusion_files/QED% ... ulsion.pdf

I have blogged about my current concept state here: http://www.orbiter-forum.com/blog.php?b=233 I would like to invite you all to comment on it.

Now my question concerns Dr. Bussards calculations for the attainable ISPs of a QED-ARC engine. In the paper above he mentions an ISP range of 1500-5500s for the ARC engine. I have run some numbers and can't quite find out how this would be possible:

Assuming a 6GW Reactor that has an electrical efficiency of 80% (i think that was about the efficiency that was assumed in the papers), that would mean 1.2GW of energy would have do be cooled regeneratively. Assuming also (like in the paper) that the reactor could still work at a temperature of 2087K and assuming LH2 as propellant:

H2 has a heat capacity of ~14300 J/(kg*K)

so the massflow required to keep the reactor at 2087K would be

mdot = 1.2e9 / (14300 * 2087) =~ 40.2 (units W * K * kg / (J * K) = kg/s)

Now when i assume the engine can convert all 6GW of reactor power to kinetic energy of the propellant i get:

eKin = 0.5 * mdot * vexhaust^2

so

vexhaust = sqrt(eKin * 2 / mdot)

vexhaust = sqrt(6e9 * 2 / 40.2) =~ 17277 (units sqrt(W * s / kg) = m/s)

ISP = vexhaust / 9.81 = 1761s (units m * s^2 / m * s = s)

So i get an absolute maximum of 1761s ISP at a reactor temperature of 2087K. So how did Bussard figure out a maximum of 5500s ? If i take that value and do the calculation in reverse i get a reactor temperature of about 20000K (!!!).

i'm in the process of developing an addon for Orbiter, the free spaceflight-simulator. (http://www.orbitersim.com)

What i want to do is a SSTO spaceplane using Polywell reactors, inspired by the design proposed by Dr. Bussard for example in this paper:

http://www.askmar.com/Fusion_files/QED% ... ulsion.pdf

I have blogged about my current concept state here: http://www.orbiter-forum.com/blog.php?b=233 I would like to invite you all to comment on it.

Now my question concerns Dr. Bussards calculations for the attainable ISPs of a QED-ARC engine. In the paper above he mentions an ISP range of 1500-5500s for the ARC engine. I have run some numbers and can't quite find out how this would be possible:

Assuming a 6GW Reactor that has an electrical efficiency of 80% (i think that was about the efficiency that was assumed in the papers), that would mean 1.2GW of energy would have do be cooled regeneratively. Assuming also (like in the paper) that the reactor could still work at a temperature of 2087K and assuming LH2 as propellant:

H2 has a heat capacity of ~14300 J/(kg*K)

so the massflow required to keep the reactor at 2087K would be

mdot = 1.2e9 / (14300 * 2087) =~ 40.2 (units W * K * kg / (J * K) = kg/s)

Now when i assume the engine can convert all 6GW of reactor power to kinetic energy of the propellant i get:

eKin = 0.5 * mdot * vexhaust^2

so

vexhaust = sqrt(eKin * 2 / mdot)

vexhaust = sqrt(6e9 * 2 / 40.2) =~ 17277 (units sqrt(W * s / kg) = m/s)

ISP = vexhaust / 9.81 = 1761s (units m * s^2 / m * s = s)

So i get an absolute maximum of 1761s ISP at a reactor temperature of 2087K. So how did Bussard figure out a maximum of 5500s ? If i take that value and do the calculation in reverse i get a reactor temperature of about 20000K (!!!).