lightbulb, launch, momentum vs. energy

[Keith Lofstrom]

I occasionally ponder first principles and assumptions.
This leads to better questions, and occasionally a
profitable invention and/or business, like those that
paid for my house and retirement.

Those who can't grok any more than a slogan or a tweet,
or fear basic algebra and high school physics, should
stop reading now. Campaign for Congress instead.

-----

I will make one basic assertion about an "integral",
which you can verify by typing "integration of powers of
x" into a web browser.

PONDERING LAUNCH: rockets generate a lot of energy, but
because they derive their momentum by spewing propellant
stored on board, rockets must use a LOT of energy to
move enough momentum (mass times velocity) to reach Earth
orbit or escape, and lift the propellant that they will
expel later in flight.

This process is horribly inefficient; even with absurdly
high ISP. Almost all the kinetic energy ends up as
propellant kinetic energy instead of vehicle kinetic
energy, roiling the atmosphere and infinitesimally
displacing planet Earth in the opposite direction.
(for fun, calculate how much).

With actual propellants, the fraction of total energy that
becomes payload kinetic and gravitational-lift energy is
absurdly tiny. If the goal is delivering a 300 kT warhead
over the pole, rocket "system efficiency" seems high, in a
"Dr. Strangelove" sense. Given that practically all large
rockets are optimized and deployed to deliver warheads,
it is no surprise that launch is messy and costly for the
projects WE care about.

Contemplate a magic lift machine: input energy is
transformed with 100% efficiency into gravitational
potential energy, with infinite mass "to push against".

The following is a "Fermi estimate"; I will round numbers
for ease of contemplation and computation; one decimal
place accuracy, ignoring complications such as air
friction and the rotation of the Earth.

How much energy would an (absurdly) ideal surface-to-earth-
-escape launch system require? Forget the implementation
details for now, simply assume we are adding gravitational
potential energy to an object until it is beyond Earth's
gravity well.

Here comes the algebra. You can skip down to the result
just before "3----------", but don't come crying to me
if you don't believe it.

1--------------------------------------------------------

Lifting one kilogram (m) one meter (Δr) vertically (Earth
radially) in a one gee (g, 9.8 m/s²) EARTH SURFACE gravity
field needs an energy input of
ΔE = m g Δr = 1 kg × 9.8 m/s² × 1 m
or 9.8 kg m²/s² or 9.8 Joules or 9.8 Watt-seconds.

Lifting one more meter requires ever-so-slightly-less
than 9.8 Joules, because gravity diminishes by inverse
square.

Let's make an equation for gravity g versus radius:
g(r) = g(re) * ( re / r )²

... where g(re) = gee = 9.8 m/s² sorta kinda.

As radius r increases towards infinity, g(r) tends
(asymptotes) towards zero.

Assuming a 6,400,000 meter radius Earth, that means
gee drops to 9.8 × (6,400,000 / 6,400,001)² m/s²
or 9.799996938 Joules. Another meter vertically,
9.799993875 Joules. Adding up those energy increments
meter by meter to infinity would take infinite time,
for a slightly inaccurate result.

Instead, calculus ... which Newton invented to solve
problems like this. Leibniz simplified and streamlined
calculus so he (and everyone else who isn't Newton but
sorta knows algebra) can understand it.

Then the French invented the metric system so that we
don't need to use horsepower and pounds and BTUs and
miles and other archaic/incompatible units. Watts,
kilograms, joules, meters. MKS. If you want to use
CGS, go orbit a grape, not a planet.

In order to sum tiny energy increments to infinity, you
use an integral, or more accurately (for us) write an
integral, then look it up the conversion to simpler
algebra using Wikipedia.

Cutting to the chase, the gravitational energy difference
from earth surface to infinity (escape energy) is

E(escape) = m * (integral from Re to infinity) g(r) dr

E(escape) = m * (int-yada-yada) ( gee * Re²/R² ) dr

We can simplify the integral by moving the constants
to the front:

E(escape) = m * gee * Re² * (int-yada-yada) ( 1/R² ) dr

The integral operation changes int( 1/R² ) to 1/R, and
and the "Re to infinity" replaces the R with Re for the
first limit, and infinity for the second:

E(escape) = m * gee * Re² * ( 1/Re - 1/infinity )

Thus:

2--------------------------------------------------------

E(escape) = m * gee * Re

I went through the math motions because your intuition
will almost certainly rebel after I plug in the numbers.

For m = 1 kg, gee = 9.8 m/s², and Re = 6,400,000 meters,

E(escape) = 62,720,000 Joules per kilogram .

Rounding up, 63 Megajoules sounds like a lot, until you
realize that one joule is a watt-second, 3600 joules is
a watt-hour, and 3,600,000 joules is a kilowatt hour.

So, E(escape) = 17.4 kilowatt hours per kilogram.

Find a recent electric bill, probably the envelope
with the bright red edges under all the other bills
you forgot to pay.

I pay Pacific Northwest hydropower rates, or more
accurately Wyoming coal power rates because Google and
Facebook and Microsoft data centers swot up all the
hydropower around here. The rate is obfuscated by a
zillion charges and taxes and credits ...

... but last month I spent $270.20 for 1345 kilowatt
hours, most of them feeding MY OWN "data center".
Model physics calculations heat my home.

That's $0.20 (twenty cents) per kilowatt hour. Hence:

E(escape) = $3.50 of electricity per kilogram (!!!)

3--------------------------------------------------------
REBELLION! MAN THE BARRICADES! KILL ALL THE ENGINEERS!

Or ... ponder better systems than rockets, alternatives
that couple acceleration forces to terra firma without a
propellant intermediary. There are many on offer, most
of them silly, none of them cheap, because a planet-scale
launch system scaled to human tolerable accelerations will
have at least one planet-scale dimension: L=V²/2a

(human tolerable acceleration ... I can deal with a six
foot drop, this laptop cannot. Gee tolerance isn't easy).

4--------------------------------------------------------
And now for "lightbulb".

I keep a few ancient filament light bulbs around as test
loads for the power supplies and power sensors that I
sometimes design. One of my favorites is an ancient
200 Watt Phillips bulb, which emits a measly 3850 lumens.
It claims to have a service life of 750 hours. 200 watts
for 750 hours is 150 Kilowatt-hours, or 540 Megajoules.

NOT including a lamp with an Edison screw socket (patented
in 1881), the bulb itself weighs 43 grams.

At 17.4 kWh/kg (17.4 Wh/g, 62.5 KJ/g) for 100% energy
efficient launch-to-escape, lifting that 43 gram bulb
from Earth surface to infinity would cost 2.7 Megajoules,
0.5% of the energy it would consume over its 750 hour
service life, or a bit less than 4 hours of illumination
power consumption.

HOW?

That's a "mere engineering problem", as my late lamented
friend Bob Forward would say. For an obsolete, about-to-
be-improved possibility, look at

http://launchloop.com

For another "mere engineering problem", design the stupid
and dangerous Edison screw base OUT of home lamp systems,
make immortal gossamer LED lamps separate from the robust
DC power supply driving them, use the entire lamp base as
a heat sink, and make the new "DC" blade socket "smart"
and childproof and 50 year durable. First application,
future space stations and spacecraft.

I hope the above will trigger my favorite (and profitable)
phrase "That won't work, but THIS WILL!" Note that 90% of
THIS WILLS won't work either; invention mostly involves
strangling cherished ideas before they embarrass you in
public. I've got file drawers full.

-----

Keith Lofstrom

-----

P.S: http: will become https, moinmoin wiki will become
mediawiki, Linux OS will move from ancient Redhat to
Debian Bookworm "REAL SOON NOW" ... a favorite ironic
computer promise popularized by my late lamented frenemy
Jerry Pournelle.

If there are Linux adepts reading this who are eager to
trade Debian sysadmin help for physics and math and old
electronics help, contact me at kei...@keithl.com .

----

Alternate bribe: The first 30 years of JBIS, the Journal
of the British Interplanetary Society, bound volumes with
some howler mis-predictions by the young Arthur C. Clarke.
That will cost partial YEARS of ADEPT sysadmin.

Sir Arthur *died* soon after demanding Fred Pohl disparage
the "Lofstrom Loop" in the novel "Beyond the Blue Event
Horizon" (4 pages of old notes by ACC, all the text written
by Fred). I am *honored* to be a named "Clarke's first
law" victim by none other than ACC himself.

The January 1948 JBIS has an amusing ACC article explaining
why interplanetary communication is impossible, due to the
huge power demanded by the vacuum tubes. At that time, Bell
Labs was sending sample germanium transistors (under NDA)
to partner companies and research institutions. Those
transistors evolved to VLSI chips, and my own inventions.

I'm old. I might croak tomorrow, or three decades from now.
I don't want those JBIS going to innumerate fools, or recycle.

Keith L.

--
Keith Lofstrom kei...@keithl.com

[Paul Werbos]

Ramon Chase was FULLY aware of these thrust versus specific impulse kind of tradeoffs. Jess sponable discussed them in his own way. Wpafb has had engineers paying attention.

Current policy "experts" in US gov managed by musk are not so clear. The unmet opportunities are there but here I wonder.

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[Keith Henson]

On Sat, Mar 8, 2025 at 6:28 PM Keith Lofstrom <kei...@keithl.com> wrote:

snip

> So, E(escape) = 17.4 kilowatt hours per kilogram.

I check your number. It is around 15 kWh to lift a kg to GEO which is
most of the way to escape and about the same energy needed to reduce
aluminum from the oxide. Of course, it takes a mechanical space
elevator which we don't know how to build. If we did,15 GW would lift
a thousand tons per hour. Launch loop is a better idea, but we don't
k know how to make those either, at least not yet.

Still, if your concern is payback time, a power satellite will repay
the energy used to launch it in a little over two months even with
rockets.

KeithH