Hello, I'm a university student who has just started learning about rocket propulsion. I was reading one of the very famous online source and came across with this formula At=Wt/Pt(RTt/γGc)^(1/2) or ( http://www.risacher.org/rocket/neq-7.png )
R is gas constant, Tt is the temperature of the gasses at nozzle throat, Gamma is the ratio of gas specific heats and Pt is the pressure.
It is supposedly a formula of calculating the area of nozzle throat but the problem is, I don't understand how one would derive that, and why there is gravity constant involved in the equation. I have 9 books on rocket propulsion sitting next to me right now, I have read all of those but still can't figure it out. The only formula that I see in most of the books and sources on the internet is http://www.lerc.nasa.gov/WWW/K-12/airpl ... mflchk.gif (formula at the very bottom). Could someone please tell me how to derive the nozzle throat area formula? Thanx in advance
Question about nozzle throat area equation
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superman12
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larry cottrill
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re: Question about nozzle throat area equation
super,
I don't know much about rockets, but I DO know the answer to ONE of your questions - what is the gravitational constant in there for?
In both the English and Metric systems, calculations involve DIFFERENT UNITS for mass and force. Unfortunately, in the English system we are used to thinking of mass in force terms: pounds [or lb], rather than the real term of mass, the slug! On the other hand, in the Metric system, we have gotten accustomed to thinking of forces in mass terms [Kg] rather than in actual terms of force, such as Newtons. Physicists generally are careful to keep their use of the units "pure", but engineers do not!
If a physicist wrote the rocket equations, the "gravitational constant" would not be used. But because we hobby "engineers" don't want to have our masses in slugs but rather in pounds [so everybody will know what we're talking about], the constant gets thrown in to make the correction. When used this way, it really isn't a gravitational correction at all - it is just a units converter. The reason it happens to be the same is because of the way it is derived. A slug is defined to weigh 32.1 lb because that is the mass that 1.0 lb of force will accelerate at 1.0 ft/sec/sec. The metric conversion factor is similarly derived for a Newton of force and 1 metre/sec/sec of acceleration, which generates a factor of 9.8 something. In both cases, the number will be precisely equal to G for the units system chosen.
L Cottrill
I don't know much about rockets, but I DO know the answer to ONE of your questions - what is the gravitational constant in there for?
In both the English and Metric systems, calculations involve DIFFERENT UNITS for mass and force. Unfortunately, in the English system we are used to thinking of mass in force terms: pounds [or lb], rather than the real term of mass, the slug! On the other hand, in the Metric system, we have gotten accustomed to thinking of forces in mass terms [Kg] rather than in actual terms of force, such as Newtons. Physicists generally are careful to keep their use of the units "pure", but engineers do not!
If a physicist wrote the rocket equations, the "gravitational constant" would not be used. But because we hobby "engineers" don't want to have our masses in slugs but rather in pounds [so everybody will know what we're talking about], the constant gets thrown in to make the correction. When used this way, it really isn't a gravitational correction at all - it is just a units converter. The reason it happens to be the same is because of the way it is derived. A slug is defined to weigh 32.1 lb because that is the mass that 1.0 lb of force will accelerate at 1.0 ft/sec/sec. The metric conversion factor is similarly derived for a Newton of force and 1 metre/sec/sec of acceleration, which generates a factor of 9.8 something. In both cases, the number will be precisely equal to G for the units system chosen.
L Cottrill
re: Question about nozzle throat area equation
Larry... beautifully explained.. thankyou..... db...
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Bruno Ogorelec
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re: Question about nozzle throat area equation
A very good question and a very good answer. A perfect example of one of the best reasons for the existence of this forum.
Larry, that was is one of the best explanations of this problem (which bothers many people) that I have seen yet. Thanks.
Larry, that was is one of the best explanations of this problem (which bothers many people) that I have seen yet. Thanks.
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superman12
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re: Question about nozzle throat area equation
Thank you everyone, and especially Larry Cottrill, for your kind replies! I now understand the reason why gravity constant is involved in the equation. A reason I never thought of before, and that might be a key of deriving the whole equation itself (which I couldn't do because I didn't know why G was involved. If anyone could still help me out with deriving the formula, that would still be great!). Thank you once again.
Best regards, superman
Best regards, superman