Author Topic: Rocket Cars  (Read 49967 times)

Offline DonPMitchell

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Rocket Cars
« on: June 17, 2008, 01:18:30 PM »
In working on my book, I've been reading some early classics like Goddard's 1919 paper and Tsiolkovsky's 1903 paper (I had to fix old slavonic letters and archaic spellings before I could even feed it to my Russian-to-English translator).  Goddard was so much more sophisticated than any of these other early guys like Oberth etc.  He did the math, and he did real experiments that were soundly designed.

One of Goddard's big achievements was combining rocket engines with de Laval nozzles, and he measured more than 64 percent efficiency in some larger engines.  Am I right in thinking that rockets are the most efficient heat engines known to man then?

If so, why not power vehicles with rocket motors instead of piston engines?  There must be some obvious reason why that is a dumb idea.
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Offline Satanic Mechanic

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Re: Rocket Cars
« Reply #1 on: June 17, 2008, 02:14:36 PM »

One of Goddard's big achievements was combining rocket engines with de Laval nozzles, and he measured more than 64 percent efficiency in some larger engines.  Am I right in thinking that rockets are the most efficient heat engines known to man then?

If so, why not power vehicles with rocket motors instead of piston engines?  There must be some obvious reason why that is a dumb idea.

Heat engine wise yes.  Some people will dispute me on these approximate numbers but the gasoline engine has an efficiency of 13%, Diesel around 24% and the highest rated Sterling engine I have ever heard of was around 30%.  I know a jet turbine is up there but I do not know what the numbers are.

Rocket car... hate to be behind one of those at a stop sign. :lol:

SM
« Last Edit: June 17, 2008, 02:17:18 PM by Satanic Mechanic »

Offline DonPMitchell

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Re: Rocket Cars
« Reply #2 on: June 17, 2008, 04:41:06 PM »
Parallel parking would be my big concern.
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Offline spacecat27

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Re: Rocket Cars
« Reply #3 on: June 17, 2008, 05:25:05 PM »
I'll bet Bob can chime in on this with some hard numbers-
My 'big picture' thinking tells me the answer is 'yes'- but the nature of rockets is for them to burn all or most of their fuel in a short period of time and then 'coast.'  Probably not practical for a wheeled vehicle unless you have the freeway all to yourself. :)

LOL- makes me think back to one of Craig Breedlove's runs in the "Spirit of America" where he sheared through a number of telephone poles before nose-diving into a canal... and lived to say, "For my next act, I'm just going to set myself on fire."   :shock:

Offline Bob B.

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Re: Rocket Cars
« Reply #4 on: June 18, 2008, 02:11:38 PM »
I'll bet Bob can chime in on this with some hard numbers-

That's a good bet. :D

A mass-reaction system, like a rocket engine, is a very poor way to drive a vehicle.  It is much better to use a mechanical system that transfers force directly to the ground, such as through drive wheels.

Think of it thing way…  Suppose you are sitting on a small wheeled cart.  Is it easier to propel yourself along by placing you hand on the ground and giving a push, or by throwing rocks to generate momentum thrust?

Suppose we are traveling on the highway at 65 MPH in a fairly typical sedan with the following measurements:

Curb Weight:  3,000 pounds
Driver & Cargo:  200 pounds
Frontal Area:  22 square feet
Drag Coefficient:  0.35

There are two forces we have to overcome:  rolling resistance and aerodynamic drag.  At highway speed on good tires, the rolling resistance is about 0.008 times the weight of the car.  Drag can be calculated from the drag equation.

In this example the rolling resistance is 25.6 lb and the drag, at sea level, is 83.2 lb.  If we are using a rocket engine, we must therefore supply a thrust of 108.8 lb to maintain a constant speed of 65 MPH.

If we’re going to use a rocket in an everyday passenger vehicle, we need to keep the complexity of the system to a minimum.  Therefore, let’s assume we’re using a monopropellant engine rather than a more complicated bipropellant engine.  We’ll get the best performance from hydrazine, but it is very toxic and dangerous.  More likely we’ll use hydrogen peroxide or nitrous oxide.  Hydrogen peroxide can be a bit unstable, but it is liquid at room temperature and is not too dangerous to handle (you’ll need heaters in the winter to keep it from freezing).

The specific impulse will depend on the engine chamber pressure and the hydrogen peroxide concentration.  The nozzle will have an expansion ratio optimized for sea level operation.  Best case, I think we might get an ISP of about 120 seconds.

At 108.8 lb thrust and an ISP of 120 sec, the fuel consumption rate is 0.9067 lb/s.  At 65 MPH it takes 55.385 s to travel one mile, therefore consuming 50.2 lb of fuel.  Hydrogen peroxide weighs 12.0 lb/gallon, so we’re burning 4.18 gallons to go one mile.  Our fuel economy is a dreadful 0.24 MPG!

Even if we use a high-pressure bipropellant system, our fuel economy is still lousy.  Suppose we could somehow get an ISP of 300 s, we’re still managing only 0.60 MPG.

(Note that these calculations assume constant mass.  In reality our mass is decreasing as the engine burns fuel.)

Offline jdbenner

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Re: Rocket Cars
« Reply #5 on: June 18, 2008, 02:45:04 PM »
Another way to look at the problem is as follows: 
Energy equals force times distance. 
Momentum is measured in force times time.
One horse power is 550 foot pounds per second.

A rocket with a constant thrust of 100 pounds moving at ten miles per hour (ruffly 15 feet per second), will be opperating at 100 pounds times 15 feet per second which is 1500 foot pounds per second, or (1500/550) 2.7 horse power. 8)

The same rocket with the same constant thrust of 100 pounds moving at 100 miles per hour (ruffly 150 feet per second) will be opperating at ten times the horse power :shock:, or ruffly 27 horse power.  100*150=15,000,  15,000/550= 27 horse power.

Only vary fast cars would be practical with rocket engines. :D

Joshua D. Benner Associate in Arts and Sciences in General Science

Offline spacecat27

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Re: Rocket Cars
« Reply #6 on: June 18, 2008, 05:22:48 PM »
Outstanding, Guys!
This is a great little discussion to pass along to youngsters and teachers- and a great refresher for oldsters such as I.

Offline DonPMitchell

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Re: Rocket Cars
« Reply #7 on: June 19, 2008, 03:37:23 PM »
jdbenner, how is that analysis different from a car driven by wheels instead of by a rocket?
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Offline jdbenner

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Re: Rocket Cars
« Reply #8 on: June 19, 2008, 04:08:47 PM »
jdbenner, how is that analysis different from a car driven by wheels instead of by a rocket?


Well, with an engine driving wheels you can use mechanical advantage. 8)  You can separate the thrust from the engine's fuel consumption.

If I need 100 pounds of force at ten miles per hour I only require 2.7 horse power, so I don't need to burn the same amount of fuel per second as I would to get 27 horse power.  With a rocket that is not possible.

A rocket is intended to impart momentum.  While momentum and energy are connected, they are not the same thing.  It does not matter if a rocket is more efficient at converting heat to the motion of its exhaust, than any other engine can convert heat to motion, if that energy is not transfered efficiently to the rocket.

P.S. A rocket in a vacuum does not operate on a closed cycle, so it can in principle convert heat energy to the kinetic energy of the exhaust with 100% efficiency.

Joshua D. Benner Associate in Arts and Sciences in General Science

Offline Bob B.

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Re: Rocket Cars
« Reply #9 on: June 19, 2008, 05:45:16 PM »
In a car you use your mechanical advantage at low speed to generate high torque at the wheels to accelerate quickly.  As you speed up, you shift gears and generate less torque but higher wheel RPMs.  The faster you go the more RPMs you're producing, but you lose acceleration because the trade off for more RPMs is less torque.  RPMs equate to speed and torque equates to acceleration, and the two are related to power by the following equation:

Power (horsepower) = Torque (foot-pounds) X Revolutions (per minute) / 5252

If your engine puts out constant power, you'll initially generate lots of torque and acceleration and you'll gradually transition to low torque and acceleration but lots of speed.

With a fixed-thrust rocket engine, you have a constant acceleration (ignoring change in mass).  As you speed up, you're producing more power, as jdbenner demonstrated.  A rocket is constant acceleration / variable power, while an internal combustion engine with transmission and driveline is constant power / variable acceleration (more or less, see edit below).

In my previous example I calculated that a thrust of 108.8 lb was required to maintain a constant highway speed of 65 MPH.  Ignoring drag and rolling resistance, a force of 108.8 applied to a 3,200-lb car yields an acceleration of only 1.094 ft/s2.  Our car would do 0 to 60 in a little over 80 seconds.  Yikes!

Of course we could use a variable thrust rocket engine.  108.8 pounds of thrust at 65 MPH works out to 10,370 ft-lb/s, or about 18.86 horsepower.  If we were to produce the same power at only 5 MPH, we'd need a thrust of 1,414 pounds.  This higher thrust would, of course, give us more acceleration (14.22 ft/s2).  If we were to vary our thrust to produce constant power, we'd have gradually decreasing acceleration just like we did with our gasoline powered car.

Unfortunately, the only way our rocket engine can produce more thrust is to burn more propellant.  When our car's internal combustion engine runs at constant power, it burns the same amount of fuel.  We are able to vary the torque to the wheels through gearing.

EDIT:

A car doesn't really have constant power.  As the engines revs up, its power increases.  When you shift gears the engine's RPMs drop, and consequently, its power output decreases.  The engine then revs back up until you shift gears again, and so on.  However, if you were to plot power versus time and draw the best fitting line through the data points, it would have a fairly flat slope.  That is, the running average of the engine's power is fairly constant.
« Last Edit: June 26, 2008, 09:19:02 AM by Bob B. »

Offline DonPMitchell

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Re: Rocket Cars
« Reply #10 on: June 25, 2008, 10:28:05 PM »
I think G. Crocco was saying this in his 1923 paper on "Super Aviation":

"To parity of weight and for jet propulsion, the fuel necessary to cover a determined distance in horizontal and uniform flight, is in inverse ratio of the product of the speed of flight for the speed of exhaust of the propulsive jet. This demonstrates the convenience of high velocity of advance; and it also demonstrates the reason of failure of the propulsor of reaction for the speeds of ordinary aviation. "

(My bad translation from Italian)

Crocco seems to have been important back then, he was basically the Goddard of cruise missiles.  Korolev talks about him a lot.
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Offline ijuin

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Re: Rocket Cars
« Reply #11 on: June 27, 2008, 01:20:22 AM »
Can you express that as a physics equation?

Offline indaco

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Re: Rocket Cars
« Reply #12 on: June 29, 2008, 12:51:07 PM »
Hy, my first message here. You'll notice my english is awful and I'll use meters, kilogram and seconds.


I'll try to describe in the most simple manner as possible why I think rocket cars are very unefficient.


In brief: 

rocket propulsion is energy efficient when veichle speed is relatively close to the exhaust speed.


Not in brief:

yes, it's true,  efficiency of a rocket engine can be very high, up to 70% (this because it works at very high temperatures and thermodinamic explains that this help).

But this is the efficiency of the engine alone, not propulsive efficiency.

An umprecise definition of it is:  ((kinetic energy in the exhausts) + (kinetic energy added to the veichle))/ (chemical energy in the propellant)

If the veichle velocity is relatively small, most of the energy is given to the exhausts, in other words is wasted.

If the veichle speed is identical to exhaust speed... the exhaust final speed will be zero, so 100% of the 70% of chemical energy from the propellant is given to the veichle.

But as tipical exhaust speeds for LOX/H2 rockets value is 4500 m/sec, that is about 10000 mph.... at pratical speeds on real roads propulsive efficiencly will be incredibly poor.

You can find the exact formula of propulsive efficiency here:  http://en.wikipedia.org/wiki/Propulsive_efficiency#Rocket_engines

I enclose the chart of propulsive efficiency for rockets, borrowed by wikipedia (Released into the public domain by the author).



v=veichle speed,  c=exhaust speed
« Last Edit: June 29, 2008, 12:53:43 PM by indaco »

Offline DonPMitchell

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Re: Rocket Cars
« Reply #13 on: June 29, 2008, 01:16:47 PM »
Quote
If the vehicle velocity is relatively small, most of the energy is given to the exhausts, in other words is wasted.

Ah ha!
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Offline jdbenner

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Re: Rocket Cars
« Reply #14 on: July 03, 2008, 02:39:56 PM »
indaco has just made the point I tried to make a while back on the thread
https://www.thespacerace.com/forum/index.php?topic=782.0

I suppose you could make the rocket car more efficient by watering down the propellant.  But the additional propellant mass and the lower thermal efficiency of the rocket engine would probably cancel any gains.

P.S.  I have wondered about saving on imported propellants (Hydrogen etc.) for Lunar launches, using oxygen extracted from the Lunar regolith, by running the rocket engines with a large surplus of oxygen.
Joshua D. Benner Associate in Arts and Sciences in General Science