# How to estimate the time it takes to generate steam?

## Main Question or Discussion Point

Hello people,

I have a question regarding the time calculation.

could you please let me know if there are any equations with which I can find the time to generate steam in the header for certain pressure level.

lets say I am supplying fuel and mass flow of water to the boiler at certain rates. how can I get the time to convert the water to steam (theoratically)

the flow is continous

Related Mechanical Engineering News on Phys.org
russ_watters
Mentor
I have a question regarding the time calculation.

could you please let me know if there are any equations with which I can find the time to generate steam in the header for certain pressure level.

lets say I am supplying fuel and mass flow of water to the boiler at certain rates. how can I get the time to convert the water to steam (theoratically)

the flow is continous
This is very similar to your previous thread, and has a similar answer: continuous processes do not have a duration. You're asking the wrong question and I don't know what question you really mean to ask.

Perhaps if you explain in more detail what you want to do and provide some numbers we can help better.

Chandrakanth_balusa
Im sorry Mr.Russer for not giving the correct question.

Iam working on the topic spinning reserve of a Generator. by calculacting the steam level in the steam header i thought I can estimate how long the generator or the turbine generator set could serve the over load demand in the crisis situations in the production plant.

for the moment I have no knowledge of numbers since its a research topic.

my intention was to know if a generator in a group suddenly trips, how is the load distributed and how long it takes to generate the boiler to provide enough steam to other generators to serve the demand.
I think it is still not clear for you.
hope you got my point?

Last edited by a moderator:
anorlunda
Staff Emeritus
That is a valid and interesting topic. However:

Your question is to confused to answer. You seem to be asking how long the generator can produce power if the fire in the furnace trips (maybe 5 seconds). Then you ask how fast other boilers in the group can respond of one generator trips. (about 2 minutes). Then you ask about spinning reserve, which is a related topic but not the same.

Even if your questions were clear, the answer is never a simple formula. Either you accept a ballpark number like 2 minutes, or you need a complete transient simulation of the power plant that may take you 6 months to write.

So please tell us more about what you are trying to accomplish. how accurate your answers must be, and how much time you have to spend on this project.

Chandrakanth_balusa and russ_watters
russ_watters
Mentor
Ahh, so you are indeed asking about a transient situation, and for a power plant. We have several power plant engineers here who can provide more help than I can, but I'll try to help frame it a little better:

-You have multiple steam turbine generators: How many, how big, are they packaged or custom built (do you have a manufacturer/documentation you can ask these questions to?), and are they fed by the same steam supply or their own separate boilers?

-One goes down, which instantaneously increases the demand on the others. So, then what?

-If they are all on the same steam supply, you have no steam capacity problem, just a control response problem. I suspect - but a power plant engineer can weigh in - that a larger power plant could rapidly adjust with almost no impact outside the plant. The main issues would be how fast the steam valve can actuate and how fast the flow increase reaches the turbine (propagating at more than 50m/s) vs the roatational inertia of the turbine and generator.

-If each has its own boiler, then the steam demand isn't shared and losing one means you now have a steam supply problem. And it's a complicated problem. You have rotational inertia in the generator/turbine and thermal inertia in the boiler and steam system. How much reserve you have depends on the size/mass of the generator and turbine, size (volume) of the boiler and piping, etc. Then how long you have before you lose to much will also depend on how big the output shortfall is. Thermodynamically the boiler ramp-up has similar thermal inertia issues.

We have several power plant engineers here, and I'm not sure who all of them are, but let's start with @anorlunda [edit; oops, he already saw it...good] and he can invite others. I will say, however, that this sounds like the type of problem that warrants serious engineering investigation, by which I mean hiring an engineering firm that specializes in power plant design to do an evaluation rather than just getting off-the-cuff answers from people with unverifiable expertise and no direct knowledge of your plant, on the internet.

Chandrakanth_balusa
That is a valid and interesting topic. However:

Your question is to confused to answer. You seem to be asking how long the generator can produce power if the fire in the furnace trips (maybe 5 seconds). Then you ask how fast other boilers in the group can respond of one generator trips. (about 2 minutes). Then you ask about spinning reserve, which is a related topic but not the same.

Even if your questions were clear, the answer is never a simple formula. Either you accept a ballpark number like 2 minutes, or you need a complete transient simulation of the power plant that may take you 6 months to write.

So please tell us more about what you are trying to accomplish. how accurate your answers must be, and how much time you have to spend on this project.
Hello Mr, Arnolunda,

my question is totally related to the spinning reserve. usually the generating limit in the generator capability curve is set by the operator by his practical experience. if his calculation goes wrong in the crisis situation all the generators would suffer the overload during the primari spinning reserve action. I thought that by knowing the steam level or based on the available steam may be we can estimate the left over spinning reserve( that the generator capability of serving the power in emergency)

for that I would like to know how long it takes for the boiler to generate the steam required for the turbine after the primary spinning reserve is done. usually its a continous process there should be no delay in supplying steam to the turbine but in this situation turbines run in lower speeds than usual.

my project is for six months and this my goal to set the generator limit in the generator capability curve not just with the experience but by providing some algorithm to that.

I have learned some thing about the steam power plant but im not able to figure it out how to end my project. I have a question in my mind if the Idea does really makes sense , or should I have to know something else other than what I know.

hope you understood my point.

sorry, if you find any difficulties understanding.

Ahh, so you are indeed asking about a transient situation, and for a power plant. We have several power plant engineers here who can provide more help than I can, but I'll try to help frame it a little better:

-You have multiple steam turbine generators: How many, how big, are they packaged or custom built (do you have a manufacturer/documentation you can ask these questions to?), and are they fed by the same steam supply or their own separate boilers?

-One goes down, which instantaneously increases the demand on the others. So, then what?

-If they are all on the same steam supply, you have no steam capacity problem, just a control response problem. I suspect - but a power plant engineer can weigh in - that a larger power plant could rapidly adjust with almost no impact outside the plant. The main issues would be how fast the steam valve can actuate and how fast the flow increase reaches the turbine (propagating at more than 50m/s) vs the roatational inertia of the turbine and generator.

-If each has its own boiler, then the steam demand isn't shared and losing one means you now have a steam supply problem. And it's a complicated problem. You have rotational inertia in the generator/turbine and thermal inertia in the boiler and steam system. How much reserve you have depends on the size/mass of the generator and turbine, size (volume) of the boiler and piping, etc. Then how long you have before you lose to much will also depend on how big the output shortfall is. Thermodynamically the boiler ramp-up has similar thermal inertia issues.

We have several power plant engineers here, and I'm not sure who all of them are, but let's start with @anorlunda [edit; oops, he already saw it...good] and he can invite others. I will say, however, that this sounds like the type of problem that warrants serious engineering investigation, by which I mean hiring an engineering firm that specializes in power plant design to do an evaluation rather than just getting off-the-cuff answers from people with unverifiable expertise and no direct knowledge of your plant, on the internet.
Hello Mr.Russ watters,

thank you again for ur valuable answer!

my project has nothing to do with the practical situation. its just a research topic which is a bit new for me to understand the thermodynamics behind the power plant operation. I am trying my best to gather all the information which takes place in the existing power plants. the book that you suggested me in my last thread helped me alot and i mean it.

I am assuming that I have a recovery boiler which servers two turbine generator sets with a steam header in between. if suppose a load demand is increased in a mill all of a sudden without any information , the generators have to supply more power than what they are doing in the moment. for that how does my generator react if it supply with lesses frequency, how long it might take to come to normal speeds(frequency).

since my plant is based on steam, the reaction time is comparatively more than the other turbines like gas.

I wanted to estimate how much more can my generator supply(i.e the spinning reserve) in this situation by doing the theoratical calculation. what I have understood from the definition of spinnig reserve is the difference of rated capacity of generator and the supplying power. but what if the boiler is not able to supply the enough steam for generator to work under full load?

hope you got my question

regards
Chandrakanth

anorlunda
Staff Emeritus
Sigh. There are a lot of issues here, and I'm afraid a few language barriers.

A generator capability curve is not something operators can set. It looks like this.

But I accept that your operators do set something you call capability. It is the maximum MW for each generator? If yes, how do they decide today where to set it?

Since you said that frequency changes with load, is it correct that the plant you are talking about has no connection to the power grid?

The limits to how fast and how much in a power plant are set by constraints. How much and how fast may the voltage change? frequency change? pressure change? drum level change? fuel flow change? temperature change? and so on. The complete answer to your question, you would need to find the limits to all those critical parameters (there may be 30-50 of them), and then calculate how they vary dynamically. Most important, you need the details on all the control systems in the plant. That means a full transient simulation of the entire plant, and it probably can't be completed in 6 months.

A second approach is to ask the manufacturer of the boilers. They may have max/min and ramp limits published for that equipment that are based on their own analysis when the equipment was designed.

A third approach is to experiment. Go to the power plant and stage some tests with step changes in the MW set point. Record all the critical parameters. Then compare those changes with the operating limits. You may then be able to extrapolate to estimate the maximum rate of change allowed. An experimental approach might well fit a six month project.

But you will not find formulas on the Internet. Nor will you get more useful answers from engineers without first supplying all of the drawings and technical information about all the equipment in the whole plant.

When engineers design equipment, they start with requirements. What must this equipment do to be successful? The same can be applied to a research project. Requirements and goals first. Define what "successful project" means.

Good luck.

Chandrakanth_balusa and russ_watters
Sigh. There are a lot of issues here, and I'm afraid a few language barriers.

A generator capability curve is not something operators can set. It looks like this.
View attachment 243230
But I accept that your operators do set something you call capability. It is the maximum MW for each generator? If yes, how do they decide today where to set it?

Since you said that frequency changes with load, is it correct that the plant you are talking about has no connection to the power grid?

The limits to how fast and how much in a power plant are set by constraints. How much and how fast may the voltage change? frequency change? pressure change? drum level change? fuel flow change? temperature change? and so on. The complete answer to your question, you would need to find the limits to all those critical parameters (there may be 30-50 of them), and then calculate how they vary dynamically. Most important, you need the details on all the control systems in the plant. That means a full transient simulation of the entire plant, and it probably can't be completed in 6 months.

A second approach is to ask the manufacturer of the boilers. They may have max/min and ramp limits published for that equipment that are based on their own analysis when the equipment was designed.

A third approach is to experiment. Go to the power plant and stage some tests with step changes in the MW set point. Record all the critical parameters. Then compare those changes with the operating limits. You may then be able to extrapolate to estimate the maximum rate of change allowed. An experimental approach might well fit a six month project.

But you will not find formulas on the Internet. Nor will you get more useful answers from engineers without first supplying all of the drawings and technical information about all the equipment in the whole plant.

When engineers design equipment, they start with requirements. What must this equipment do to be successful? The same can be applied to a research project. Requirements and goals first. Define what "successful project" means.

Good luck.
Hello Mr.Arnolunda

Recently I have been to a Automation supplying comapany, there I came to know that the operator sets in their Generator management system each generator a limit not to generate power more then prescribed.

I am a Paper Engineer and my approach is mostly towards Paper mills which have their own power generating facility using the recovery boilers. so, this limit will be set by the operator according to his own exerience with that particular Generator and plant. so this limit is set assuming that there is enough steam supply so that he can generate untill that limit. my question here is that if his assumption was wrong and if he increases the load on that generator then it may lead to trip because of the frequency issues.

so I want to measure the steam level available in the system and then may be I can relate that with the amount of power can be generated with which the limit can be set being sure that no frequency issues takes place.

now if I am able to measure the excess steam in the system I think this could workout, but my doubt is that does the system always generate excess steam than required? if yes can the steam header before the turbine able to accomodate tha excess steam? if then I can measure that steam can I consider that as my energy or spinning reserve?

my assumptions in this project would be the plant is in island mode and it has only steam turbines.

thanks alot for your valuable responses!

regards
Chandrakanth

anorlunda
Staff Emeritus
Thank you for the clarifications.

now if I am able to measure the excess steam in the system I think this could workout, but my doubt is that does the system always generate excess steam than required? if yes can the steam header before the turbine able to accomodate tha excess steam? if then I can measure that steam can I consider that as my energy or spinning reserve?
I'll refer back to post #4
You seem to be asking how long the generator can produce power if the fire in the furnace trips (maybe 5 seconds). Then you ask how fast other boilers in the group can respond of one generator trips. (about 2 minutes). T
I see it as two questions.
1. So, if by excess steam in the headers, you mean how long can the turbine make useful power after the furnace flame trips, just a few seconds.
2. The separate question, if one boiler trips, how long until neighboring boilers can make up the loss, the answer is a minute or two.
So step one is to decide which is the correct question (maybe both), and whether the order of magnitude answers (seconds or minutes) are useful. Be more specific on what scenario you are studying, trip of the flame in a furnace, or trip of one generator's circuit breaker?

There could be a third scenario. One boiler flame trips, but we use the energy stored in the water drums (not the steam headers). We allow the pressure to drop as that water boils to continue to make steam for tens of seconds. That case will be terminated when the pressures get too low, or the drum water levels get too high, and that will probably happen before the frequency gets too low. Everything becomes interdependent and complicated in such scenarios.

Then as step two, decide if it is important that the answers be accurate. For example, for question 1, does it really matter if the answer is 2 seconds or 3 seconds? For question 2, does it matter if the answer is 2 minutes or 1.5 mintues? If yes, then more detailed calculations are justified. If no, then there is no point of detailed calculations.

Recently I have been to a Automation supplying comapany, there I came to know that the operator sets in their Generator management system each generator a limit not to generate power more then prescribed.
That also confuses me. Such a limit would be a static limit steady-state limit. It is only remotely associated with transient dynamics. I do not understand how the answers to your calculations will influence how those limits are set.

Do you know how to calculate how fast the frequency changes when generation and load are unbalanced? Do you know at what frequency, things trip?

Chandrakanth_balusa and russ_watters
Thank you for the clarifications.

I'll refer back to post #4

I see it as two questions.
1. So, if by excess steam in the headers, you mean how long can the turbine make useful power after the furnace flame trips, just a few seconds.
2. The separate question, if one boiler trips, how long until neighboring boilers can make up the loss, the answer is a minute or two.
So step one is to decide which is the correct question (maybe both), and whether the order of magnitude answers (seconds or minutes) are useful. Be more specific on what scenario you are studying, trip of the flame in a furnace, or trip of one generator's circuit breaker?

There could be a third scenario. One boiler flame trips, but we use the energy stored in the water drums (not the steam headers). We allow the pressure to drop as that water boils to continue to make steam for tens of seconds. That case will be terminated when the pressures get too low, or the drum water levels get too high, and that will probably happen before the frequency gets too low. Everything becomes interdependent and complicated in such scenarios.

Then as step two, decide if it is important that the answers be accurate. For example, for question 1, does it really matter if the answer is 2 seconds or 3 seconds? For question 2, does it matter if the answer is 2 minutes or 1.5 mintues? If yes, then more detailed calculations are justified. If no, then there is no point of detailed calculations.

That also confuses me. Such a limit would be a static limit steady-state limit. It is only remotely associated with transient dynamics. I do not understand how the answers to your calculations will influence how those limits are set.

Do you know how to calculate how fast the frequency changes when generation and load are unbalanced? Do you know at what frequency, things trip?
1. So, if by excess steam in the headers, you mean how long can the turbine make useful power after the furnace flame trips, just a few seconds.
2. The separate question, if one boiler trips, how long until neighboring boilers can make up the loss, the answer is a minute or two.
Hi Mr.Anorlunda,

my question was not about the trip of Furnace or Boiler, but if in a sudden the load is increased on the generator then the primary spinning reserve will comes into action for few seconds as per some literatures i have read. my question is does the steam header have extra steam to serve this generator in terms of spinning reserve?

so the capability curve i have seen looks like this where the line in red colour is set by the operator and he does on the assumption that turbine can serve only upto that limit. but what if the steam in header is not in the level to serve turbine to reach that limit?

my ultimate goal is to measure the steam in the system(Excess steam) on which we can rely in the emergency situation like sudden increase in load.

thank you again for ur time and response!

anorlunda
Staff Emeritus
We are getting closer. A sudden change in load is normal, it happens all the time. Only the size of the change determines if it is normal or emergency.

When you get a sudden increase in load, the frequency drops, the turbine speed governor opens the throttle valve to let in more steam. That causes the steam pressure in the headers to drop, and yes there are a few seconds of energy storage in the header. The drop in pressure causes more boiling in the drum to produce steam. There is much more energy in the form of hot water in the drum than steam in the headers; enough for 1-2 minutes. The boiler control system will increase the fuel flow, and will adjust the feedwater flow. Everything is interdependent.

So how far can you push that whole thing; how much load change? Like I said, it is not just frequency. It is all the pressure, temperature, and water level limits that might be the most limiting.

None of that relates to the maximum MW limit shown by that red line. Why do you think it does?

#### Attachments

• 41.5 KB Views: 103
Chandrakanth_balusa
Hallo Anorlunda,

now I understood the process behind this steam system. but my concern is that I wanted to measure that energy available in the hot water. and relate it directly to the output of the turbine. do u have any recommendations like a book or an article where I can find the details about this consequences in emergency situation.

the red line in the curve I think is the limit set by the operator to make sure the generating power does not go above that level. however sudden increase in load may lead to all these changes in pressure, frequency and mass flow of steam and turbine may not have enough supply of steam from the header to reach this operator limit.

thank you for fast responses!

regards
Balusa

jim hardy
Gold Member
2019 Award
Dearly Missed
Spinning reserve ? A rule of thumb for power system operators is

you want to apportion power among your plants so the highest loaded generator is producing not more than 10% of your total system load at the time.
The reason for that is
should that heaviest loaded generator trip
it's only a 10% step change in load for all the others to make up, which they can do easily within a second.
That way frequency won't get low enough for automatic relays to shed customers - you see, they get mad at their power company when it happens.

So it's more a practical than theoretical question

Energy flows into the boilers as fuel, is turned into thermal and passed through the turbogenerators and out to the customers as electrical
you have thermal inertia of the boiler
you have rotating inertia of the turbogenerators
and you have rotating inertia of all those refrigerator and airconditioner compressors out in world customer-land.

so you can write the differential equations for that energy flow in units of your choice
just as you did in your Diff-Eq class for fluid flow down a series of tanks.

Inertia constant for turbogenerators is published in their application manual because the power system planners like @anorlunda need it
thermal inertia of a boiler is huge and i have never tried to estimate it -
rotating inertia of consumer appliances is decreasing with inverter driven compressors now
and rotating inerftia of windmills i have been trying to pry out of GE and Siemens for years but it's been hard to find a sales guy who understands the question -

so it's a challenging time to be a power system analyst.

Please share whet you find here ?

old jim

Last edited:
russ_watters
Spinning reserve ? A rule of thumb for power system operators is

you want to apportion power among your plants so the highest loaded generator is producing not more than 10% of your total system load at the time.
The reason for that is
should that heaviest loaded generator trip
it's only a 10% step change in load for all the others to make up, which they can do easily within a second.
That way frequency won't get low enough for automatic relays to shed customers - you see, they get mad at their power company when it happens.

So it's more a practical than theoretical question

Energy flows into the boilers as fuel, is turned into thermal and passed through the turbogenerators and out to the customers as electrical
you have thermal inertia of the boiler
you have rotating inertia of the turbogenerators
and you have rotating inertia of all those refrigerator and airconditioner compressors out in world customer-land.

so you can write the differential equations for that energy flow in units of your choice
just as you did in your Diff-Eq class for fluid flow down a series of tanks.

Inertia constant for turbogenerators is published in their application manual because the power system planners like @anorlunda need it
thermal inertia of a boiler is huge and i have never tried to estimate it -
rotating inertia of consumer appliances is decreasing with inverter driven compressors now
and rotating inerftia of windmills i have been trying to pry out of GE and Siemens for years but it's been hard to find a sales guy who understands the question -

so it's a challenging time to be a power system analyst.

Please share whet you find here ?

old jim
Dear Old Jim,

I appreciate your response regarding the spinning reserve.

I have raised a small question about spinning reserve in the system. what actually does it mean? is it jus the difference of rated capacity and the power being generated? this I have learned from the books and articles on the internet.

but i think its the inertia of the boiler, turbine and generator as u said. so can we really estimate it by writing differential equation of energy flow ?

thanks and regards!

Balusa

jim hardy
Gold Member
2019 Award
Dearly Missed
is it jus the difference of rated capacity and the power being generated?
yes, that'd be it. Think of it as that much generation already warm, up to steam pressure and speed, so all you have to do is open the throttle valves . Throttle valves are driven by hydraulic servomotors and capable of very fast motion, well under a second . The boiler's inertia provides energy during time it takes for fuel and air flows to respond - they're slower , on order of a few seconds (more than one less than ten).
So boiler response will be an initial sag in pressure then recovery hopefully with perfect damping ie barely perceptible overshoot.

but i think its the inertia of the boiler, turbine and generator as u said. so can we really estimate it by writing differential equation of energy flow ?
Sure, you have an energy inventory in each part of the machine, and inflow and an outflow

instead of mass flowrates use BTU or kiloJoule flowrates.

That's all a power plant is - a machine that transports energy, changing its form along the way-
from chemical (or nuclear) to thermal to mechanical finally to electrical

coal has maybe 10,000 btu/lb
steam energy content you get from steam tables, nuke plant maybe 800 psi ~1200BTU/lb
fossil more like 1000F 2400psi maybe 1460BTU/lb
a BTU is 778 ft-lbs
and a kilowatt hour is 3412.7 BTU or 2.66e6 million (oops) ft-lbs

lots of conversions here
https://www.engineeringtoolbox.com/
the principle is easy but the units make your equations look messy

if i ever did such a calculation it was around 1970 and you'll understand that memory fades over time

you ought to give it a try
i did such things in days of Basic on a TI99 home computer with for-next loops using finite difference approach
for second = 0 to 10,000
Qin = (coal flow rate}
..
..
..'
Qout = (kilowatts)
print (variables of interest)
next second

calculating energy inventories , pressures and temperatures along the way

turn each value of interest into a string variable of length 132(the width of my printer set to small font), spaces(Chr$20h) with an asterisk(Chr$2Ah) at nth position along the line
n was (value of variable divided by range of variable) X 132
doing that scales your output to width of printer paper
So printing a line every X seconds gives you a graph of variable vs time when you turn the paper sideways.
With old fanfold printers you could make a graph a whole room wide

how i miss those simple days when we understood our tools..
Wish i'd kept that TI99.

old jim

Last edited:
Chandrakanth_balusa
Chestermiller
Mentor
Hello people,

I have a question regarding the time calculation.

could you please let me know if there are any equations with which I can find the time to generate steam in the header for certain pressure level.

lets say I am supplying fuel and mass flow of water to the boiler at certain rates. how can I get the time to convert the water to steam (theoratically)

the flow is continous

So this is start-up of a boiler?

yes it could be considered so..

yes, that'd be it. Think of it as that much generation already warm, up to steam pressure and speed, so all you have to do is open the throttle valves . Throttle valves are driven by hydraulic servomotors and capable of very fast motion, well under a second . The boiler's inertia provides energy during time it takes for fuel and air flows to respond - they're slower , on order of a few seconds (more than one less than ten).
So boiler response will be an initial sag in pressure then recovery hopefully with perfect damping ie barely perceptible overshoot.

Sure, you have an energy inventory in each part of the machine, and inflow and an outflow

instead of mass flowrates use BTU or kiloJoule flowrates.

That's all a power plant is - a machine that transports energy, changing its form along the way-
from chemical (or nuclear) to thermal to mechanical finally to electrical

coal has maybe 10,000 btu/lb
steam energy content you get from steam tables, nuke plant maybe 800 psi ~1200BTU/lb
fossil more like 1000F 2400psi maybe 1460BTU/lb
a BTU is 778 ft-lbs
and a kilowatt hour is 3412.7 BTU or 2.66e6 million (oops) ft-lbs

lots of conversions here
https://www.engineeringtoolbox.com/
the principle is easy but the units make your equations look messy

if i ever did such a calculation it was around 1970 and you'll understand that memory fades over time

you ought to give it a try
i did such things in days of Basic on a TI99 home computer with for-next loops using finite difference approach
for second = 0 to 10,000
Qin = (coal flow rate}
..
..
..'
Qout = (kilowatts)
print (variables of interest)
next second

calculating energy inventories , pressures and temperatures along the way

turn each value of interest into a string variable of length 132(the width of my printer set to small font), spaces(Chr$20h) with an asterisk(Chr$2Ah) at nth position along the line
n was (value of variable divided by range of variable) X 132
doing that scales your output to width of printer paper
So printing a line every X seconds gives you a graph of variable vs time when you turn the paper sideways.
With old fanfold printers you could make a graph a whole room wide

how i miss those simple days when we understood our tools..
Wish i'd kept that TI99.

old jim
Hello Old Jim,

I understood this so called spinning reserve or the boiler inertia practically.
But, are there any good source that you know where I can learn about these inertia equations theoratically?

the information you have given untill now was very very helpful for me in understanding.
I thank you so much for your help and support!

regards
Balusa

jim hardy
Gold Member
2019 Award
Dearly Missed
But, are there any good source that you know where I can learn about these inertia equations theoratically?