> From: Steven Bonneville <bonnevil@...>

Agreed! There are ways of getting "instantaneous" acceleration,

>

> ehenry@... (Eric Henry) wrote:

> > i have come to the conclusion that I don't get it.

> [...]

> > How do I apply Isp, or Vexhaust, to determine how many Gs of acceleration my

> > ship can do?

>

> You don't. Isp is a measure of *fuel efficiency*; how many seconds of

> one Newton thrust you get per Newton of fuel burned. To determine how

> many Gs of acceleration your ship can do, you need to know how massive

> it is (which changes, as you use fuel) and how much thrust your engine

> provides. [Incidentally, this means rockets can accelerate harder

> once they've burned some fuel and vehicle mass decreases.]

> For example, there are ion engines with high fuel efficiency (Isp) but

> low thrust, and solid rockets with low fuel efficiency but high thrust.

but they often rely on other bits of info that are not

readily available.

Ai = (Mdot * g * Isp) / Mc

where:

Ai = "instanteneous" accelleration in m/sec^2

Mdot = propellant mass flow in kg/sec (very hard to look this up)

g = one gravity of acceleration = 9.81 m/sec^2

Isp = propulsion system's specific impulse in seconds

Mc = ship's current mass at this instant in time

(which will change as propellant is expended)

F = Mdot * g * Isp

where:

F = thrust in Newtons or kg mt/sec

In other words, Ai = F / Mc

In case you are interested, Ve = g * Isp, where Ve = velocity of

exhaust. So F = Mdot * Ve

The MU that Mr. Watt was using appears to be based more on

deltaV instead of thrust. Thus your confusion.

What is often more useful (if travel time is of secondary consideration)

is a propulsion system's delta-V. This is the total amount of

change in velocity the drive can inflict on the ship, if all the

propellant is expended. It is measured in meters per second (m/sec).

(You'll see this in novels like ANTARES RISING, where the ensign

tells the captain that the ship has 200 m/sec deltaV left in the

propellant tanks.)

At NASA, they measure energy requirements for various space missions

in terms of the delta-V required.

deltaV = g * Isp * 1n[Lambda]

where:

deltaV = velocity change in m/sec

g = one gravity of acceleration = 9.81 m/sec^2

Isp = propulsion system's specific impulse in seconds

1n[x] = take the natural logarithm of x

Lambda = ship's current "mass ratio"

Lambda = Mt / Me

where:

Mt = ship's total mass (including current load of propellant)

Me = ship's mass without propellant

(Mass ratios tend to be from 2 to 10. Ships with a mass ratio

of 10 are huge flimsy tinfoil soap bubbles holding titanic

amounts of propellant)

Note that the deltaV equation does not include a time component.

Thus it cannot tell the difference between a low thrust ion drive

that will take years to get to the target, and a high thrust

chemical rocket.

You may find the equations below to be useful. Or maybe not.

* WARNING * The below equations assume a constant acceleration,

which is not true for a ship expending mass (for instance,

propellant). Ai = F/Mc so as the ship's mass goes down, the acceleration

goes up.

============================================

When you have two out of three of average velocity (Va) in m/sec,

change in distance (S) in meters or time (T) in seconds

Va = S / T

S = Va * T

T = S / Va

============================================

When you have two out of three of acceleration (A) in m/sec^2,

change in velocity (V) in m/sec or time (T) in seconds

A = V / T

V = A * T

T = V / A

============================================

When you have two out of three of change in distance (S) in meters,

acceleration (A) in m/sec^2, or time (T) in seconds

plus Initial Velocity (Vi) Note: if deaccelerating, acceleration A is negative

S = (Vi * T) + ((A * (T^2)) / 2)

A = (S - (Vi * T)) / ((T^2) / 2)

T = (sqrt[(Vi^2) + (2 * A * S)] - Vi) / A

If Vi = 0 then

S = (A * (T^2)) / 2

A = (2 * S) / (T^2)

T = sqrt[(2 * S) / A]

============================================

When you have two out of three of change in distance (S),

acceleration (A), or final velocity (Vf)

plus Initial Velocity (Vi) Note: if Vf < Vi, then A will be negative

(deacceleration)

S = (Vf^2 - Vi^2) / (2 * A)

A = (Vf^2 - Vi^2) / (2 * S)

Vf = sqrt[Vi^2 + (2 * A * S)]

If Vi = 0 then

S = (Vf^2) / (2 * A)

A = (Vf^2) / (2 * A)

Vf = sqrt[2 * A * S]

============================================

If the ship constantly accelerates to the midpoint, then

deaccelerates to arrive with zero velocity at the

destination:

T = 2 * sqrt[S / A]

S = (A * (T^2)) / 4

A = (4 * S) / (T^2)- Did I mention i'm a Poli Sci major? :)

So, to sum up, Are most / all of the near future technology rockets

incapable of escaping earth? However, a good "gas mileage" in the form of

specific impulse (Isp) is the greater issue, assuming these rockets can

first be lifted / assembled to orbit via some other means.

Are solid fuel rockets the only ones that can escape earth?

My understanding is that liquid fuel rockets are capable of a constant

acceleration even as the mass of the rocket declines as fuel is spent. Are

we capable of fine control of acceleration or it gross control only.

Any spreadsheets out there. Will trade Hipparcos data formatted for

Nyrath's stereostar.

-----Original Message-----

Subject: Re: [sfconsim-l] Physics for Poli Sci majors, excluding Chris W of

course. > From: ehenry@... (Eric Henry)

Nope. I'm not sure that solid rockets were even used for manned flights

>

> Did I mention i'm a Poli Sci major? :)

>

> So, to sum up, Are most / all of the near future technology rockets

> incapable of escaping earth? However, a good "gas mileage" in the form of

> specific impulse (Isp) is the greater issue, assuming these rockets can

> first be lifted / assembled to orbit via some other means.

>

> Are solid fuel rockets the only ones that can escape earth?

until Shuttle. Saturn V used liquid hydrogen/liquid oxygen for the upper

stages, and kerosene/liquid oxygen in the first stage.

> My understanding is that liquid fuel rockets are capable of a constant

The SSME (Space Shuttle Main Engine) rockets on the orbiter use liquid

> acceleration even as the mass of the rocket declines as fuel is spent. Are

> we capable of fine control of acceleration or it gross control only.

hydrogen and can be throttled. The older F-1 rockets on the first stage

of a Saturn V burned kerosene and were fixed-thrust. The disadvantage

of a fixed-thrust rocket is that you can't throttle it back as you burn

fuel, so you accelerate harder, and harder.... The Shuttle doesn't hit

the same peak acceleration as Saturn V, which means more people meet the

physical requirements to fly on the Shuttle.

The SRBs are a slightly different story. Once ignited you don't have

any control over them; they just burn until they go out. However, they

are manufactured to reduce thrust after they've been burning for a while,

so that the spacecraft isn't put through too much stress. So in a sense

they are fixed-thrust, but you can design them to have different amounts

of pre-selected thrust during the burn.

-- Steve Bonneville- On Tue, Aug 10, 1999 at 10:54:19 AM, Steven Bonneville <bonnevil@...>

wrote:

> The SRBs are a slightly different story. Once ignited you don't have any

Note that some solid fuel rockets have exhaust ports which can be opened to

> control over them; they just burn until they go out. However, they are

> manufactured to reduce thrust after they've been burning for a while, so

> that the spacecraft isn't put through too much stress. So in a sense

> they are fixed-thrust, but you can design them to have different amounts

> of pre-selected thrust during the burn.

effectively cut their thrust, by letting the gases escape the chamber in many

directions rather than simply through the rear. I do not believe they are

designed to be throttled, but I suppose they could be.

One of the things to keep in mind about solid rockets is that they don't burn

from the middle, but rather from the inside out. The burning reaction is a

function of surface area, so many of these rockets have hollow spaces that are

shaped like stars rather than simple cylinders. A cylinder would have a

greater surface area as the fuel burned, thereby increasing thrust; the star

shape keeps the surface area approximately the same.

FYI.

chrisw