^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
------------------------------------------------------------------------------
X-Sender: S9421793@mail.student.utwente.nl Mime-Version: 1.0
Date: Mon, 13 May 1996 19:02:39 +0100
To: KellySt@aol.com, kgstar@most.fw.hac.com, stevev@efn.org, 
jim@bogie2.bio.purdue.edu, zkulpa@zmit1.ippt.gov.pl,
hous0042@maroon.tc.umn.edu, rddesign@wolfenet.com,
David@InterWorld.com, lparker@destin.gulfnet.com, DotarSojat@aol.com,
neill@foda.math.usu.edu, 101765.2200@compuserve.com,
MLEN3097@Mercury.GC.PeachNet.EDU
From: T.L.G.vanderLinden@student.utwente.nl (Timothy van der Linden) 

Subject: Re: Physic help

>>I personally find it not a stange number at all, it shows very clear what
part of the initial mass can be converted to energy (for
anti-matter&matter mixture f=1, or said differently, all mass can be
converted to energy). 

>True, after you do the calculation, but initself not a very helpfull number. 
>In this case, its sort of an intermediate step in a calculation, rather than
a usefull result in itself. Also kind of confusing. 

It is certainly not an intermediate number in a calculation. I think it is
one of the most important numbers when one compares fuels needed for
interstellar space travel. (Compare this to the density of different
substances, it is a fundamental property and not just some number that
turns up after you devide the weight by the volume.) 

-=- -=- -=- -=- -=- -=- -=- -=- -=- -=- -=- -=- -=- -=- -=- -=- -=- -=-
-=- 

>The lit programs I used were the ones that calculated the specific
impulse when given a exaust velocity, and the ones for calculating the
terminal speed/fuel mass ration/specific impulse. Give 2 of the three and
it figures out the third. There were actually 2 of the latter programs (both
for staged and single stage craft) and the numbers were close. 

That program uses the classic rocket equation that is also used for
chemical rocket engines:

M=M0 Exp(Vend/Vexh)

This formula assumes that all fuel can be used as reaction mass, as long
as you use chemicals the error is no very significant, but when using
fusion fuel a measurable part of the fuel is converted to energy and thus
cannot be used as reaction mass.
It is mainly this that causes the rather large error, besides that
relativistics also plays a small role that probably causes another small
deviation.

>I don't see how energy content of the fuel would effect the calculations,
since that wasn't an imput. Only the exaust velocity or specific impulse. 

That's exactly what I mean, the program didn't even bother to figure out
what kind of fuel was used.

Timothy





^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
------------------------------------------------------------------------------

Date: Wed, 15 May 96 16:40:27 +0200
From: zkulpa@ippt.gov.pl (Zenon Kulpa)
To: KellySt@aol.com, hous0042@maroon.tc.umn.edu, 
T.L.G.vanderLinden@student.utwente.nl, stevev@efn.org,
jim@bogie2.bio.purdue.edu, zkulpa@ippt.gov.pl, rddesign@wolfenet.com,
David@interworld.com, lparker@destin.gulfnet.com, DotarSojat@aol.com,
sl0c8@cc.usu.edu, MLEN3097@Mercury.GC.PeachNet.EDU,
101765.2200@compuserve.com, kgstar@most.fw.hac.com 

Subject: Re: Re: The future...etc.
Cc: zkulpa@lksu.ippt.gov.pl

>From kgstar@most.fw.hac.com Wed May 15 16:18:57 1996 

>Did we ever discus this idea? Any interest? 

>Kelly

>>Date: Mon, 18 Mar 1996 17:47:57 -0500
>>From: DotarSojat@aol.com

>>What would you think about modifying the purpose of the Project
slightly? In a Reusable Launch Vehicle Study I ran 30 years ago (my, how
time flies!), we had a purpose you might consider for this Project. The
purpose was (paraphrased, because the Report is in my office 26 miles
away, and I don't plan on going in there in the near future) (1) to make an
internally consistent comparison of the different options, with conceptual
design only in enough detail to allow rating them regarding feasibility and
cost, and (2) to determine the advancements in technology in relation to
current levels required to make them achievable.


My proposal to compile a "Design Space" survey, was directed roughly
toward the same goal, esp. the point (1) above, in addition to provide a
sort of summary of our previous discussions and achievements.
After my first, very fragmentaric sketch, Kelly attempted to write an
extended version which he posted on our list and put on his WWW pages.
However, his version is more like his personal opinion on certain issues
(some of them quite controversial among us here) rather than impartial
summary of the discussions or awailable options. It (like my sketch) also
does not cover the full "design space" anyway. Thus more work towards
the Design Space idea would be necessary. If only I had more time :-( I
would attempt to prepare my extended version of it, or at least comment
extensively on Kelly's... 

As to the point (2) above, we also briefly started something along this
line - remember short discussion originated by me on technological
progress in propulsion, AI and nanotechnology necessary to make the
starship idea workable?

So, generally, I am FOR making the Dotar idea a central issue of our work
here...

Regards,

-- Zenon






^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
------------------------------------------------------------------------------
X-Sender: kgstar@pophost.fw.hac.com
Mime-Version: 1.0
Date: Wed, 15 May 1996 10:21:50 -0500
To: zkulpa@ippt.gov.pl (Zenon Kulpa)
From: kgstar@most.fw.hac.com (Kelly Starks x7066 MS 10-39) 

Subject: Re: Re: The future...etc.
Cc: KellySt@aol.com, hous0042@maroon.tc.umn.edu, 
T.L.G.vanderLinden@student.utwente.nl, stevev@efn.org,
jim@bogie2.bio.purdue.edu, zkulpa@ippt.gov.pl, rddesign@wolfenet.com,
David@interworld.com, lparker@destin.gulfnet.com, DotarSojat@aol.com,
sl0c8@cc.usu.edu, MLEN3097@Mercury.GC.PeachNet.EDU,
101765.2200@compuserve.com, kgstar@most.fw.hac.com,
zkulpa@lksu.ippt.gov.pl

At 4:40 PM 5/15/96, Zenon Kulpa wrote:
>>From kgstar@most.fw.hac.com Wed May 15 16:18:57 1996 

>>Did we ever discus this idea? Any interest? 

>>Kelly

>>>Date: Mon, 18 Mar 1996 17:47:57 -0500 From: DotarSojat@aol.com

>>>What would you think about modifying the purpose of the Project
slightly? In a Reusable Launch Vehicle Study I ran 30 years ago (my, how
time flies!), we had a purpose you might consider for this Project. The
purpose was (paraphrased, because the Report is in my office 26 miles
away, and I don't plan on going in there in the near future) (1) to make an
internally consistent comparison of the different options, with conceptual
design only in enough detail to allow rating them regarding feasibility and
cost, and (2) to determine the advancements in technology in relation to
current levels required to make them achievable.


>My proposal to compile a "Design Space" survey, was directed roughly
toward the same goal, esp. the point (1) above, in addition to provide a
sort of summary of our previous discussions and achievements.
>After my first, very fragmentaric sketch, Kelly attempted to write an
extended version which he posted on our list and put on his WWW pages.
However, his version is more like his personal opinion on certain issues
(some of them quite controversial among us here) rather than impartial
summary of the discussions or awailable options. It (like my sketch) also
does not cover the full "design space" anyway. Thus more work towards
the Design Space idea would be necessary. If only I had more time :-( I
would attempt to prepare my extended version of it, or at least comment
extensively on Kelly's... 

Yeah, I was expecting more reaction or counter inputs to my draft of the
Web page stuff. I even brought up the idea of cross referncing to peoples
'minority opinion papers' on contraversial stuff. I tried to be balenced, but
that doesn't help much if their are basic contradictions. 

>As to the point (2) above, we also briefly started something along this
line - remember short discussion originated by me on technological
progress in propulsion, AI and nanotechnology necessary to make the
starship idea workable?

>So, generally, I am FOR making the Dotar idea a central issue of our work
here...

>Regards,

>-- Zenon


Kelly


---------------------------------------------------------------------- 

Kelly Starks	Internet: kgstar@most.fw.hac.com
Sr. Systems Engineer
Magnavox Electronic Systems Company
(Magnavox URL: http://www.fw.hac.com/external.html) 







^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
------------------------------------------------------------------------------
Date: Thu, 16 May 1996 14:42:25 -0400
From: DotarSojat@aol.com
To: T.L.G.vanderLinden@student.utwente.nl, KellySt@aol.com,
stevev@efn.org, 
jim@bogie2.bio.purdue.edu, zkulpa@zmit1.ippt.gov.pl,
hous0042@maroon.tc.umn.edu, rddesign@wolfenet.com,
David@interworld.com, lparker@destin.gulfnet.com Cc: sl0c8@cc.usu.edu,
101765.2200@compuserve.com, MLEN3097@peachnet.edu, 
kgstar@most.fw.hac.com


Subject: Re: Physic help

To Kelly

Beware of using chemical-rocket parameters for fusion/antimatter
rockets. The parameter to be most wary of is the specific im- pulse, "Isp."
Isp is the rocket-engine thrust per unit mass flow rate (out of the nozzle).

We are interested in an equation that gives the velocity incre- ment,
"delta-V," of the rocket stage in terms of the ratio of the initial mass of
the stage to the final mass, the "mass ratio". The equation is called the
"rocket equation" in the West and the "Tsiolkovsky equation" in Russia
(after the first person to derive it). The depletion in mass (initial mass
minus final mass) for a chemical rocket stage is solely propellant. For a
fusion/antimatter rocket, however, the mass depletion is the sum of the
propellant mass (out of the "nozzle," or accelerator) and the mass
converted to energy in the fusion or matter/antimatter- annihilation
reaction.

For a chemical rocket stage, the parameter that links the delta-V with the
function of the mass ratio (the natural log) is simply the exhaust velocity,
Vexh, i.e.,

delta-V = Vexh ln(mass ratio) .

[Isp was invented, I believe, to allow English-system (foot-pound- second)
engineers to talk about rocket performance with metric- system
(meter-kilogram-second) engineers by "non-dimensionalizing" the exhaust
velocity. This was done by dividing it by the cons- tant gc, i.e.,

Vexh/gc = Isp .

This reduces the units to "seconds", which are common to both sys- tems.
The constant gc is only incidentally equal in value to the standard
acceleration of gravity; it is properly referred to as the conversion factor
from mass to force units, either 32.17405 lbmass-ft/(sec^2-lbforce) or
9.80665 kgmass-m/(sec^2-kgforce). (To be totally correct, the units of
Isp should be lbforce-sec/ lbmass or kgforce-sec/kgmass, but the ratios
lbforce/lbmass and kgforce/kgmass are usually just left out of both Isp
and gc.)] 

For a fusion/antimatter rocket, additional parameters that must be
included in the rocket equation are the ratio of the fusion/anti- matter
mass to the mass converted to reaction energy (Timothy's "f") and the
efficiency of conversion of reaction energy to ex- haust kinetic energy
(let's call it "eta"). Also, the velocity increment must be put into
relativistic terms. The relativistic fusion/antimatter rocket equation
becomes much more complicated than the chemical rocket equation, i.e.,
the increment in apparent velocity is given by

delta-V/c = tanh[(gexh eta/[(eta) + f(gexh - 1)]) * 
(Vexh/c) ln(mass ratio)]
where
gexh = sqrt[1 - (Vexh/c)^2]

or the increment in proper velocity is given by 

delta-U/c = sinh[(gexh eta/[(eta) + f(gexh - 1)]) * 
(Vexh/c) ln(mass ratio)]

(Note: for fusion, i.e., f greater than 1, the (eta) term does not appear
because some of the fusion reaction products can be used as propellant.)

In the case where f = 1 (matter/antimatter annihilation), the rel-
ativistic rocket equation becomes

delta-U/c = sinh[(gexh eta/[eta + gexh - 1] * 
(Vexh/c) ln(mass ratio)]

In the simplistic antimatter-rocket case where eta = 1 (100 per- cent
conversion of reaction energy to exhaust kinetic energy), the relativistic
rocket equation reduces to 

delta-U/c = sinh[(Vexh/c) ln(mass ratio)] 

in a form somewhat similar to the chemical rocket equation. (Note that all
velocities are non-dimensionalized now by dividing them by c.)

I hope this properly expresses the shortcomings of using chemical- rocket
performance relations for fusion/antimatter rockets. 

Rex











^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
------------------------------------------------------------------------------
X-Sender: kgstar@pophost.fw.hac.com
Mime-Version: 1.0
Date: Thu, 16 May 1996 14:22:56 -0500
To: DotarSojat@aol.com
From: kgstar@most.fw.hac.com (Kelly Starks x7066 MS 10-39) 

Subject: Re: Physic help
Cc: T.L.G.vanderLinden@student.utwente.nl, KellySt@aol.com,
stevev@efn.org, 
jim@bogie2.bio.purdue.edu, zkulpa@zmit1.ippt.gov.pl,
hous0042@maroon.tc.umn.edu, rddesign@wolfenet.com,
David@interworld.com, lparker@destin.gulfnet.com, sl0c8@cc.usu.edu,
101765.2200@compuserve.com, MLEN3097@peachnet.edu,
kgstar@most.fw.hac.com

At 2:42 PM 5/16/96, DotarSojat@aol.com wrote: 
>To Kelly

>Beware of using chemical-rocket parameters for fusion/antimatter
rockets. The parameter to be most wary of is the specific im- pulse, "Isp."
Isp is the rocket-engine thrust per unit mass flow rate (out of the nozzle).

>We are interested in an equation that gives the velocity incre- ment,
"delta-V," of the rocket stage in terms of the ratio of the initial mass of
the stage to the final mass, the "mass ratio". The equation is called the
"rocket equation" in the West and the "Tsiolkovsky equation" in Russia
(after the first person to derive it). The depletion in mass (initial mass
minus final mass) for a chemical rocket stage is solely propellant. For a
fusion/antimatter rocket, however, the mass depletion is the sum of the
propellant mass (out of the "nozzle," or accelerator) and the mass
converted to energy in the fusion or matter/antimatter- annihilation
reaction.

I realize that with fusion or anti-matter reactions you lose a little of the
mass to energy. But, since in the case of fusion, the fraction lost is less
than 1% of the total mass. I assumed the equation would give acceptable
accuracy. Since most of the reference examples I have, use specific
impulse and Exaust vel. I tried to stick with them out of familiarity. You
have to admit they are convenent terms. 

I'm more concerned for the MAJOR differences Tim and I get when
calculating fuel mass ratios. The fraction of a % of mass lost to energy
conversion doesn't seem to account for more than a tiny fraction of our
100 to 1 vs 150 to 1 mass ratio disagreement. (I'm obviously just looking
for rough order of magnetude numbers at this stage.) 


>For a chemical rocket stage, the parameter that links the delta-V with
the function of the mass ratio (the natural log) is simply the exhaust
velocity, Vexh, i.e.,

>delta-V = Vexh ln(mass ratio) .

>[Isp was invented, I believe, to allow English-system (foot-pound-
second) engineers to talk about rocket performance with metric- system
(meter-kilogram-second) engineers by "non-dimensionalizing" the exhaust
velocity. This was done by dividing it by the cons- tant gc, i.e.,

>Vexh/gc = Isp .

>This reduces the units to "seconds", which are common to both sys- tems.
The constant gc is only incidentally equal in value to the standard
acceleration of gravity; it is properly referred to as the conversion factor
from mass to force units, either 32.17405 lbmass-ft/(sec^2-lbforce) or
9.80665 kgmass-m/(sec^2-kgforce). (To be totally correct, the units of
Isp should be lbforce-sec/ lbmass or kgforce-sec/kgmass, but the ratios
lbforce/lbmass and kgforce/kgmass are usually just left out of both Isp
and gc.)] 

Hum, interesting bit of history. ;)


>For a fusion/antimatter rocket, additional parameters that must be
included in the rocket equation are the ratio of the fusion/anti- matter
mass to the mass converted to reaction energy (Timothy's "f") and the
efficiency of conversion of reaction energy to ex- haust kinetic energy
(let's call it "eta"). Also, the velocity increment must be put into
relativistic terms. The relativistic fusion/antimatter rocket equation
becomes much more complicated than the chemical rocket equation, i.e.,
the increment in apparent velocity is given by

>delta-V/c = tanh[(gexh eta/[(eta) + f(gexh - 1)]) * 
>(Vexh/c) ln(mass ratio)]
>where
>gexh = sqrt[1 - (Vexh/c)^2]

>or the increment in proper velocity is given by 

>delta-U/c = sinh[(gexh eta/[(eta) + f(gexh - 1)]) * 
>(Vexh/c) ln(mass ratio)]

>(Note: for fusion, i.e., f greater than 1, the (eta) term does not appear
because some of the fusion reaction products can be used as propellant.)

>In the case where f = 1 (matter/antimatter annihilation), the rel-
ativistic rocket equation becomes

>delta-U/c = sinh[(gexh eta/[eta + gexh - 1] * 
>(Vexh/c) ln(mass ratio)]

>In the simplistic antimatter-rocket case where eta = 1 (100 per- cent
conversion of reaction energy to exhaust kinetic energy), the relativistic
rocket equation reduces to 

>delta-U/c = sinh[(Vexh/c) ln(mass ratio)] 

>in a form somewhat similar to the chemical rocket equation. (Note that
all velocities are non-dimensionalized now by dividing them by c.)

>I hope this properly expresses the shortcomings of using chemical-
rocket performance relations for fusion/antimatter rockets. 

>Rex

Nice equations, but a little much for use on my hand calculator. ;) Thou I
suppose I could fire up the free sudo-copy of Mathmatica that Apple now
gives away with its operating system. If I load those equations in I should
get some nice graphs.

Kelly


---------------------------------------------------------------------- 

Kelly Starks	Internet: kgstar@most.fw.hac.com
Sr. Systems Engineer
Magnavox Electronic Systems Company
(Magnavox URL: http://www.fw.hac.com/external.html) 

----------------------------------------------------------------------












^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
------------------------------------------------------------------------------
X-Sender: S9421793@mail.student.utwente.nl Mime-Version: 1.0
Date: Thu, 16 May 1996 23:31:42 +0100
To: KellySt@aol.com, kgstar@most.fw.hac.com, stevev@efn.org, 
jim@bogie2.bio.purdue.edu, zkulpa@zmit1.ippt.gov.pl,
hous0042@maroon.tc.umn.edu, rddesign@wolfenet.com,
David@InterWorld.com, lparker@destin.gulfnet.com, DotarSojat@aol.com,
neill@foda.math.usu.edu, 101765.2200@compuserve.com,
MLEN3097@Mercury.GC.PeachNet.EDU
From: T.L.G.vanderLinden@student.utwente.nl (Timothy van der Linden) 

Subject: Physics help

Hi Kelly,

Rex letter made me look back at out letters from last week. 

When I use the following numbers:

Vexh=0.0667c (2E7 m/s)
dV =0.3c (9E7 m/s)

and the classic rocket formula:

M=Exp[dV/Vexh]

I get:

M=90

and not the 148 (or 150) you seemed to get. 

Is this the reason for the confusion that had arised? 


Timothy













^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
------------------------------------------------------------------------------
X-Sender: kgstar@pophost.fw.hac.com
Mime-Version: 1.0
Date: Fri, 17 May 1996 08:42:57 -0500
To: T.L.G.vanderLinden@student.utwente.nl (Timothy van der Linden) From:
kgstar@most.fw.hac.com (Kelly Starks x7066 MS 10-39) 

Subject: Re: Physics help
Cc: KellySt@aol.com, kgstar@most.fw.hac.com, stevev@efn.org, 
jim@bogie2.bio.purdue.edu, zkulpa@zmit1.ippt.gov.pl,
hous0042@maroon.tc.umn.edu, rddesign@wolfenet.com,
David@InterWorld.com, lparker@destin.gulfnet.com, DotarSojat@aol.com,
neill@foda.math.usu.edu, 101765.2200@compuserve.com,
MLEN3097@Mercury.GC.PeachNet.EDU

At 11:31 PM 5/16/96, Timothy van der Linden wrote: 
>Hi Kelly,

>Rex letter made me look back at out letters from last week. 

>When I use the following numbers:

>Vexh=0.0667c (2E7 m/s)
>dV =0.3c (9E7 m/s)

>and the classic rocket formula:

>M=Exp[dV/Vexh]

>I get:

>M=90

>and not the 148 (or 150) you seemed to get. 

>Is this the reason for the confusion that had arised? 


>Timothy

Well thats part of it. It certainly doesn't give me a warm comfident
feeling when our numbers are that far apart! Eiather we're talking about
something fundamentally different and don't realize it, one of us has a
blown calculator, or one of us is badly misappling some equation. 

Kelly


---------------------------------------------------------------------- 

Kelly Starks	Internet: kgstar@most.fw.hac.com
Sr. Systems Engineer
Magnavox Electronic Systems Company
(Magnavox URL: http://www.fw.hac.com/external.html) 

----------------------------------------------------------------------











^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
------------------------------------------------------------------------------
X-Sender: kgstar@pophost.fw.hac.com
Mime-Version: 1.0
Date: Fri, 17 May 1996 09:37:28 -0500
To: T.L.G.vanderLinden@student.utwente.nl (Timothy van der Linden) From:
kgstar@most.fw.hac.com (Kelly Starks x7066 MS 10-39) 



Subject: Re: Physics help (I found it!)
Cc: KellySt@aol.com, kgstar@most.fw.hac.com, stevev@efn.org, 
jim@bogie2.bio.purdue.edu, zkulpa@zmit1.ippt.gov.pl,
hous0042@maroon.tc.umn.edu, rddesign@wolfenet.com,
David@InterWorld.com, lparker@destin.gulfnet.com, DotarSojat@aol.com,
neill@foda.math.usu.edu, 101765.2200@compuserve.com,
MLEN3097@Mercury.GC.PeachNet.EDU

I found it!!


>At 11:31 PM 5/16/96, Timothy van der Linden wrote: 
>>Hi Kelly,

>>Rex letter made me look back at out letters from last week. 

>>When I use the following numbers:

>>Vexh=0.0667c (2E7 m/s)
>>dV =0.3c (9E7 m/s)

>>and the classic rocket formula:

>>M=Exp[dV/Vexh]

>>I get:

>>M=90

>>and not the 148 (or 150) you seemed to get. 

>>Is this the reason for the confusion that had arised? 


>>Timothy

>Well thats part of it. It certainly doesn't give me a warm comfident
feeling when our numbers are that far apart! Eiather we're talking about
something fundamentally different and don't realize it, one of us has a
blown calculator, or one of us is badly misappling some equation. 

>Kelly

Wait a minutte?!! The rocket equation (as cut from one of Rex's lates
E-mails) is:


Vend = the velocitie at the end of the acceleration burn or the Delta V in
our case.

Vexh = the exhaust velocity

M = starship mass (= Mi initially; = Mbo at burnout) 

Now from the rocket equation

Mi/Mbo = exp(Vend/Vexh)

And your numbers tim were:

dV = Vend =0.3c (9E7 m/s)
Vexh	=0.0667c (2E7 m/s)

Mi/Mbo = exp (9/2) = exp(4.5) = 90

I however wasn't computing a Vend of .3c. I was computing to 1/3rd c, I.E.
10E7 m/s.

Mi/Mbo = exp (10/2) = exp(5) = 148

We were both talking about something fundamentally differnt, but didn't
know it! The difference was all due to the slightly different Delta V. The
Exponential makes a hellish difference given even slight differnces in the
speed assumptions.

(See why I always want to see examples with numbers and units with your
equations Tim?)

So a 55 to 1 fuel ratio with a Vexh of 2E7 m/s: 

55 = exp (?/2E7)

or

2e7 * Ln (55) = 80E6 = .267c

So we can still get a burn down from over 1/4th c with the same fuel
ratio. Giving a touch under 17 years for a flight time to Alpha C. Much
better than I was afraid of.

:)


Kelly


---------------------------------------------------------------------- 

Kelly Starks	Internet: kgstar@most.fw.hac.com
Sr. Systems Engineer
Magnavox Electronic Systems Company
(Magnavox URL: http://www.fw.hac.com/external.html)