How to calculate the necessary delta velocity by rocket equation?

[HelmutK]

Hello,

I am a beginner to rocket physics and I would like to know how I can calculate the delta velocity which is required for a flight of a rocket in an angle of 60° which has a horizontal velocity of 200 m/s at its top and gets up to 50 km.

The goal is to design the rocket with an optimal staging. Let's assume the rocket is 1 ton heavy.

If I know my necessary delta velocity, I can use the formulas for staging the rocket. But how can I calculate this delta velocity which has to compose of the altitude of 50 km and 200 m/s on its top?

Normally these values are given like the escape velocity of 11,2 km/s , so I could make my rocket design - but now I do not know the delta velocity I need.

I really appreciate any help of you guys.

Thanks so much!
Helmut

 

[Antares JS]

Your desire to fly the rocket at an angle of 60° is a huge red flag that makes me and probably anyone else who has read your post reluctant to help you.

 

[SharkWhisperer]

Seems to me Helmut isn't planning unsafe model rocketry practices, but instead is trying to do the appropriate research into basic projectile physics as a learning lesson.

Then again, he could be a shill for Kim Jong Un's warfare programs who's picking the brains of America's missile elites! Perhaps targeting Japan, Guam, and/or the Australian beef & wine company HQs requires his calculations be worked out at precisely 60 degrees off-vertical?

*Little does he know, that his project will be a failure unless all aspects of his missile construction involves Gorilla Spray Adhesive!!!

 

[Steve Shannon]

i advise that you study trigonometry.

I guess I don’t really understand the question. This time it sounds like either you’re asking for help making a weapon or doing your homework. I’m just going to lurk.

 

[rocket_troy]

I suspect what you're fundamentally asking is what extra dV do you require to achieve your stated objectives in addition to the products provided from the rocket equation ie. from gravity and aerodynamic forces.
The answer is: you need to plug your vehicle (geometry) and its weights and its total impulse and thrust profile etc into a flight simulator to gather those answers.
Either that or familiarise yourself quite intimately with pretty much every equation in this paper: https://ntrs.nasa.gov/api/citations/20010047838/downloads/20010047838.pdf

TP

 

[SharkWhisperer]

The answer is: you need to plug your vehicle (geometry) and its weights and its total impulse and thrust profile etc into a flight simulator to gather those answers.
Either that or familiarise yourself quite intimately with pretty much every equation in this paper: https://ntrs.nasa.gov/api/citations/20010047838/downloads/20010047838.pdf

TP

Outstanding reference! I can swing with the basic geometric and algebraic questions (mostly), but Calculus? Sheesh, stopped at 1 semester and forgot precisely everything within moments after turning in my final exam. But clearly remember thinking of all kinds of cool calculations that could be done with calculus, and told myself I could relearn the vital parts again if I ever needed to. Uhhh, hasn't happened yet....

 

[rocket_troy]

I guess I don’t really understand the question. This time it sounds like either you’re asking for help making a weapon or doing your homework. I’m just going to lurk.

Actually, I think you got it right Steve. I re-read the question after my post and I think it was I who mis-interpreted although it wasn't the most comprehensible of questions.

TP

 

[PhilC]

Outstanding reference! I can swing with the basic geometric and algebraic questions (mostly), but Calculus? Sheesh, stopped at 1 semester and forgot precisely everything within moments after turning in my final exam. But clearly remember thinking of all kinds of cool calculations that could be done with calculus, and told myself I could relearn the vital parts again if I ever needed to. Uhhh, hasn't happened yet....

After 40 years in aerospace engineering & research the best advice I can give is to work on your maths. Just about every problem seems to to come back to calculus or vectors at some point.

 

[SharkWhisperer]

After 40 years in aerospace engineering & research the best advice I can give is to work on your maths. Just about every problem seems to to come back to calculus or vectors at some point.

Gee, thank you too much for that swell and insightful advice, Phil. Over decades in medical research I've used math (not "maths" on this side of the water) extensively, advanced statistics mostly for assessing clinical trial data for drugs and medical devices. Calculus? Never. Hadn't much need for a solid calculus foundation (I thought) in all the LPR/MPR that I do, either. But I'll get right on it now that you've enlightened me.

Will you be my special calculus buddy/tutor? In exchange I could teach you how to cook up a barracuda after you shoot a 5-foot spear through his gills and ride him like a pony while trying to ram your kill knife into his tiny (calculating) brain so you can take him home with all your limbs still intact and not hemorrhaging.

 

[PhilC]

Gee, thank you too much for that swell and insightful advice, Phil. Over decades in medical research I've used math (not "maths" on this side of the water) extensively, advanced statistics mostly for assessing clinical trial data for drugs and medical devices. Calculus? Never. Hadn't much need for a solid calculus foundation (I thought) in all the LPR/MPR that I do, either. But I'll get right on it now that you've enlightened me.

Will you be my special calculus buddy/tutor? In exchange I could teach you how to cook up a barracuda after you shoot a 5-foot spear through his gills and ride him like a pony while trying to ram your kill knife into his tiny (calculating) brain so you can take him home with all your limbs still intact and not hemorrhaging.

Somehow I can't see myself shooting and cooking Barracuda in Wales, but thanks for the offer

About midway through my first degree I realized that most processes in engineering are described by first or second order differential equations. in the mid 70s I was fortunate to be taught math (see, I'm learning to speak American!) by a bloke called Ken Stroud. He wrote two math books that cover the essentials of engineering math using programmed learning. Instead of the usual pages of equations his books teach by taking you through loads of examples with answers. They're called 'Engineering Mathematics' and 'Further Engineering Mathematics' and are still in print and dirt cheap. If you really want to get your head around the rocket equation, stability and all the other essential theory of rockets then book 1 is a must.

 

[SharkWhisperer]

Somehow I can't see myself shooting and cooking Barracuda in Wales, but thanks for the offer

About midway through my first degree I realized that most processes in engineering are described by first or second order differential equations. in the mid 70s I was fortunate to be taught math (see, I'm learning to speak American!) by a bloke called Ken Stroud. He wrote two math books that cover the essentials of engineering math using programmed learning. Instead of the usual pages of equations his books teach by taking you through loads of examples with answers. They're called 'Engineering Mathematics' and 'Further Engineering Mathematics' and are still in print and dirt cheap. If you really want to get your head around the rocket equation, stability and all the other essential theory of rockets then book 1 is a must.

Thanks, Phil. Appreciate the references on maths (see, I'm learning Brit? UK English, too). No cuda in Wales but your waters have those wacky blue European lobsters that I imagine are just as tasty! Keep your eye to the sky tomorrow or the next--I'm going to pop off a few birds before sunset and the prevailing westerly winds are picking up---might send a few your way on oversized chutes (probably by accident)!

 

[OverTheTop]

I've used math (not "maths" on this side of the water)

Math is an abbreviation, maths is a contraction. The normal convention when using an abbreviation is to follow it with a full stop. Contractions can be used without the full stop. I never figured why the drift from maths to math happened.

Anyway enough thread drift about mathematics and English. Any other answers for the OP? I would suggest getting open rocket simulator and using that to see what can be achieved. Alternatively Kerbel Space Program may work, but I have not used it at all.

 

[SharkWhisperer]

Math is an abbreviation, maths is a contraction. The normal convention when using an abbreviation is to follow it with a full stop. Contractions can be used without the full stop. I never figured why the drift from maths to math happened.

Anyway enough thread drift about mathematics and English. Any other answers for the OP? I would suggest getting open rocket simulator and using that to see what can be achieved. Alternatively Kerbel Space Program may work, but I have not used it at all.

They're both equally correct/incorrect. Both derived from the Latin “mathematica” (singular) and mathematicae (plural). No "S"s. And both are abbreviations; neither is a contraction. Both uses evolved around the same time, separately.

Mathematics is a mass noun, which by definition is a singular, not a plural noun, that means the science of a collection of numbers and shapes. It could also be argued that it is a plural noun referring to the collection of all mathematical sciences (trig, algebra, calculus...). Is "linguistics" plural or a singular mass noun? What's the singular if you say it's plural? The adjective "linguistic"? What's the plural of information, another mass noun? Not "informations" because that's nonsensical in all English-speaking nations (though a common mistake with ESL learners). English is a conundrum of twisted and evolved/devolved word constructions and uses. Through, threw, thorough, tho... One of the more difficult languages to learn as an adult ESL learner.

They are both equally correct, for the exact same reason---because they are both human shortcut inventions.

Back on topic--Like Over-the-Top said (even if he was a little confused about "maths" being a contraction), Open Rocket is great free software for a newcomer/returnee to plot out anticipated flights using kit rockets and different motors, and also for assisting in creating and predicting the flight characteristics of your own rocket designs. If you don't have it on your puter, you'll need to download a Java extension so you can open the program, which is simple to do. If you opt to download Open Rocket (or buy more advanced RockSim) and need any help then there's plenty of people here who will be happy to assist you.

 

[PhilC]

Before we drift too far off station I'll return to your original question.

The rocket equation is only really concerned with the efficiency of the rocket motor. In your context it relates the amount of propellant required to the efficiency of the motor. It is very useful as a hypothetical model of the perfect rocket motor operating in an environment where there are no other factors acting on the rocket. Once you bring that motor into the real world then a number of factors come into play.

The problem you're addressing is really one of kinematics. Every article about launching seems to start with the three forces acting on the rocket: Thrust, drag and weight. Most stop with a very basic treatment of each but for serious launches to space there is a lot of underlying complexity for each force.

Thrust will vary with altitude. Ideally the exhaust pressure at the nozzle should match the surrounding atmosphere otherwise the flow will expand incorrectly (called 'over' or 'under' expansion). As the rocket climbs the pressure of the surrounding atmosphere will cause the motors efficiency to change with altitude. Motors are usually designed to be at their most efficient at a particular altitude, and choosing that altitude will affect the propellant budget.

Overcoming atmospheric drag will require a significant amount of additional propellant. Launching at 60 degrees requires a longer period in the atmosphere than a vertical launch and hence even more propellant will be required to overcome drag. Drag depends strongly on atmospheric density and velocity and these relationships are far from linear. The wind profile as the rocket traverses the atmosphere can cause lateral 'drag forces' and result in potentially large perturbations on the final location and velocity when launching to space.

The direction and magnitude of the weight vector are affected by many factors. The Earth's gravitational field decreases slightly with altitude. Also, the earth is not a homogeneous sphere so the value of local gravitational acceleration is not constant across the world. These factors become significant if you want to launch to an accurate orbit insertion point.

An oft-ignored factor in this type of discussion is that final velocity needs to be relative to something. Escape velocity is usually defined relative to an inertial earth rather than a rotating earth. I won't wander off into orbital dynamics, but the choice of coordinate systems is very important when defining the purpose of a launch.

 

[SharkWhisperer]

Before we drift too far off station I'll return to your original question.

The rocket equation is only really concerned with the efficiency of the rocket motor. In your context it relates the amount of propellant required to the efficiency of the motor. It is very useful as a hypothetical model of the perfect rocket motor operating in an environment where there are no other factors acting on the rocket. Once you bring that motor into the real world then a number of factors come into play.

The problem you're addressing is really one of kinematics. Every article about launching seems to start with the three forces acting on the rocket: Thrust, drag and weight. Most stop with a very basic treatment of each but for serious launches to space there is a lot of underlying complexity for each force.

Thrust will vary with altitude. Ideally the exhaust pressure at the nozzle should match the surrounding atmosphere otherwise the flow will expand incorrectly (called 'over' or 'under' expansion). As the rocket climbs the pressure of the surrounding atmosphere will cause the motors efficiency to change with altitude. Motors are usually designed to be at their most efficient at a particular altitude, and choosing that altitude will affect the propellant budget.

Overcoming atmospheric drag will require a significant amount of additional propellant. Launching at 60 degrees requires a longer period in the atmosphere than a vertical launch and hence even more propellant will be required to overcome drag. Drag depends strongly on atmospheric density and velocity and these relationships are far from linear. The wind profile as the rocket traverses the atmosphere can cause lateral 'drag forces' and result in potentially large perturbations on the final location and velocity when launching to space.

The direction and magnitude of the weight vector are affected by many factors. The Earth's gravitational field decreases slightly with altitude. Also, the earth is not a homogeneous sphere so the value of local gravitational acceleration is not constant across the world. These factors become significant if you want to launch to an accurate orbit insertion point.

An oft-ignored factor in this type of discussion is that final velocity needs to be relative to something. Escape velocity is usually defined relative to an inertial earth rather than a rotating earth. I won't wander off into orbital dynamics, but the choice of coordinate systems is very important when defining the purpose of a launch.

Exceptionally clear and concise descriptions and explanation. Nice.

 

[MClark]

It’s been almost Three weeks and OP is nowhere to be seen.