NameOmitted
Topic Author
Posts: 722
Joined: Sun Oct 23, 2016 7:59 pm

### The math behind twins.

For starters, I am not questioning the math, that's been settled by people who are much more knowledgeable than myself. I am just trying to understand it.

One of the issues with moving jet turbines into other settings is that they are only efficient at near maximum capacity. From BBD's JetTrain to the Queen Mary 2, jet turbines are used for maximum power output, but when the vehicle is at harbor speed (or yard speed), different engines are used.

For a twin, each engine needs to be powerful enough to operate the aircraft should the other fail, at the most vulnerable point in the flight. Each engine, therefore, needs to be rated to double the thrust for what would normally be needed. Since turbines are not nearly as efficient when they are not at near full thrust, it would seem that the engines of a twin airliner spend almost their entire operating life at an inefficient power setting. What am I missing?

Starlionblue
Posts: 19497
Joined: Fri Feb 27, 2004 9:54 pm

### Re: The math behind twins.

You're missing the effect of air density varying with altitude. As the aircraft climbs, the air becomes less dense, decreasing mass flow. The engines still operate at 80-90% of maximum during the cruise and climb, but given the lower mass flow, you get less than a third of the sea level thrust.

Still in the "efficient zone". Just less thrust produced. If you look in the fine print, you'll see that the nominal thrust figure for an engine is for sea-level static thrust, meaning when the engine is standing still, at sea level, in a standard atmosphere.

One corollary is that if you lose an engine at takeoff, you can still climb on the other. On the other hand, if you lose an engine in the cruise, you will most likely have to descend quite a bit because the available thrust on one engine is far too low to maintain cruise altitude. At heavy weights a widebody cruising at 36000 feet might have to descend to 23000 feet.
Last edited by Starlionblue on Fri Nov 29, 2019 12:59 am, edited 1 time in total.
"There are no stupid questions, but there are a lot of inquisitive idiots." - John Ringo

NameOmitted
Topic Author
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Joined: Sun Oct 23, 2016 7:59 pm

### Re: The math behind twins.

Starlionblue wrote:
Turbofans operate at 80-90% of maximum during the cruise and climb. As the aircraft climbs, the air becomes less dense, decreasing mass flow. So even at 80-90% of max, you get less than a third of the sea level thrust...

Thank you.

Dalmd88
Posts: 2961
Joined: Fri Jul 28, 2000 3:19 am

### Re: The math behind twins.

NameOmitted wrote:
For starters, I am not questioning the math, that's been settled by people who are much more knowledgeable than myself. I am just trying to understand it.

One of the issues with moving jet turbines into other settings is that they are only efficient at near maximum capacity. From BBD's JetTrain to the Queen Mary 2, jet turbines are used for maximum power output, but when the vehicle is at harbor speed (or yard speed), different engines are used.

For a twin, each engine needs to be powerful enough to operate the aircraft should the other fail, at the most vulnerable point in the flight. Each engine, therefore, needs to be rated to double the thrust for what would normally be needed. Since turbines are not nearly as efficient when they are not at near full thrust, it would seem that the engines of a twin airliner spend almost their entire operating life at an inefficient power setting. What am I missing?

I think your statement about ship using different powerplants for low speed is incorrect. Most ships that use jet turbines for power use the turbine to produce electrical energy. This is used to power electric motors to propel the ship as well as all the other electric needs of the ship. I recall being on one giant Royal Caribbean cruise ship. I met the Chief Engineer and asked about the powerplants. He said they had two GE motors which were based on the CF6 core to produce all of the power for the ship, including propulsion . Most of the time one could produce enough power for the ship.

Diesel locomotives work the same way. The diesel motor is not directly connected to the wheels like a truck. The diesel runs a generator which powers the electric track motors to propel the train.

NameOmitted
Topic Author
Posts: 722
Joined: Sun Oct 23, 2016 7:59 pm

### Re: The math behind twins.

Dalmd88 wrote:
I think your statement about ship using different powerplants for low speed is incorrect. Most ships that use jet turbines for power use the turbine to produce electrical energy. This is used to power electric motors to propel the ship as well as all the other electric needs of the ship. I recall being on one giant Royal Caribbean cruise ship. I met the Chief Engineer and asked about the powerplants. He said they had two GE motors which were based on the CF6 core to produce all of the power for the ship, including propulsion . Most of the time one could produce enough power for the ship.

Thank you for the opportunity to hop down a plesant morning rabbit hole. I had been unfamiliar with Royal Caribbean ships.
You are correct, they do have a few that appear only turbine driven. In both the cases I cite, the generating capacity of the turbines are supplemented by diesel, which serves when the electrical draw is less then the bade load of a turbine.

thegrew
Posts: 16
Joined: Mon Aug 20, 2018 6:45 am

### Re: The math behind twins.

Dalmd88 wrote:

Diesel locomotives work the same way. The diesel motor is not directly connected to the wheels like a truck. The diesel runs a generator which powers the electric track motors to propel the train.

I appreciate this is slightly pedantic but that isn't the case for all diesel locomotives. You find both diesel-electric which is as you described as well as diesel-mechanical transmission that works through a more conventional gearbox.

Sent from my moto g(7) plus using Tapatalk

gloom
Posts: 347
Joined: Thu Jun 30, 2016 4:24 pm

### Re: The math behind twins.

Dalmd88 wrote:
Most ships that use jet turbines for power use the turbine to produce electrical energy. This is used to power electric motors to propel the ship as well as all the other electric needs of the ship.

I'd say it depends on ship. On warships, they usually use CODAG (Diesel And Gas working on same shaft), or CODOG (Diesel Or Gas on same shaft). There are diesel-gas turbine-electric plants, but mostly where quietness of such solution matters (submarine hunters, see Type 23 frigates with their CODLAG as example). Cruise ships with turbines are exactly as described - usually gas turbine-electric.
Are we offtoping too far?

Cheers,
Adam

Woodreau
Posts: 1825
Joined: Mon Sep 24, 2001 6:44 am

### Re: The math behind twins.

Sure, I'll help continue the off topic divergence.

My last ship - a destroyer - had 4 gas turbine engines connected to two propellers through reduction gears. or COGAG - combined gas turbine and gas turbine.

Since the engines constantly produce "thrust" the props turned at 55 rpm whenever the engines were on which allowed the ship to travel between 0 and 12 knots. To go faster than 12 knots, increase the engine thrust by advancing the TLA levers at the control station, which could be the remote control station on the bridge, the remote control station at CCS (engineering central control station) or each of the 4 engines had their own individual local control in the main engineering space.
Bonus animus sit, ab experientia. Quod salvatum fuerit de malis usu venit judicium.

flipdewaf
Posts: 3061
Joined: Thu Jul 20, 2006 6:28 am

### Re: The math behind twins.

thegrew wrote:
Dalmd88 wrote:

Diesel locomotives work the same way. The diesel motor is not directly connected to the wheels like a truck. The diesel runs a generator which powers the electric track motors to propel the train.

I appreciate this is slightly pedantic but that isn't the case for all diesel locomotives. You find both diesel-electric which is as you described as well as diesel-mechanical transmission that works through a more conventional gearbox.

Sent from my moto g(7) plus using Tapatalk

There is also diesel hydraulic, gives accurate control and high torque at low speed.

Fred

Sent from my iPhone using Tapatalk

NameOmitted
Topic Author
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Joined: Sun Oct 23, 2016 7:59 pm

### Re: The math behind twins.

Woodreau wrote:
Since the engines constantly produce "thrust" the props turned at 55 rpm whenever the engines were on which allowed the ship to travel between 0 and 12 knots.

So, to be clear, you are telling us that she would do 12 knots while essentially at idle?

Is that with one of her plants running?

gloom
Posts: 347
Joined: Thu Jun 30, 2016 4:24 pm

### Re: The math behind twins.

NameOmitted wrote:
So, to be clear, you are telling us that she would do 12 knots while essentially at idle?

Not really so. I think it's like variable pitch, constant speed propellers in planes. Depending on speed and power, it will adjust pitch to give whatever is required.

Cheers,
Adam

NameOmitted
Topic Author
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Joined: Sun Oct 23, 2016 7:59 pm

### Re: The math behind twins.

gloom wrote:
NameOmitted wrote:
So, to be clear, you are telling us that she would do 12 knots while essentially at idle?

Not really so. I think it's like variable pitch, constant speed propellers in planes. Depending on speed and power, it will adjust pitch to give whatever is required.

Cheers,
Adam

This is not my tread for being clear. Obviously, she could do LESS than 12 knots using a cvp propeller, no one would design a ship that couldn't get into port, but the post seemed to indicate that the idle speed of the turbines could produce enough thrust to propel her at 12 knots, at what amounts to their losest setting.

Woodreau
Posts: 1825
Joined: Mon Sep 24, 2001 6:44 am

### Re: The math behind twins.

NameOmitted wrote:
So, to be clear, you are telling us that she would do 12 knots while essentially at idle?

Is that with one of her plants running?

Leaving and entering port, all 4 engines will be online and the electrical network split unless there is some engineering casualty which prevents all 4 engines being online.
with all 4 engines at idle at 100% pitch, the ship will do 12 knots.

To go slower, the blade pitch will be reduced - with the ship tied up alongside the pier when engineering is ready to answer bells, prior to taking in all lines and getting underway the props will be turning 55rpm at 0 pitch.
Bonus animus sit, ab experientia. Quod salvatum fuerit de malis usu venit judicium.

JayinKitsap
Posts: 1661
Joined: Sat Nov 26, 2005 9:55 am

### Re: The math behind twins.

The trend in industry is to go diesel electric or turbine electric. Gearbox cost, life, and chance of epic fails must be considered. The newer motor technology it is the way to go.

426Shadow
Posts: 174
Joined: Tue Sep 11, 2007 8:13 am

### Re: The math behind twins.

Dalmd88 wrote:
I think your statement about ship using different powerplants for low speed is incorrect. Most ships that use jet turbines for power use the turbine to produce electrical energy. This is used to power electric motors to propel the ship as well as all the other electric needs of the ship. I recall being on one giant Royal Caribbean cruise ship. I met the Chief Engineer and asked about the powerplants. He said they had two GE motors which were based on the CF6 core to produce all of the power for the ship, including propulsion . Most of the time one could produce enough power for the ship.

Diesel locomotives work the same way. The diesel motor is not directly connected to the wheels like a truck. The diesel runs a generator which powers the electric track motors to propel the train.

I think that engineer was blowing smoke up your ass. The Oasis class are the newest and biggest ships Royal Caribbean has and this is what I found: "Oasis of the Seas is equipped with a total of six Wärtsilä 46 engines, three 12-cylinder and three 16-cylinder engines, generating more than 96 MW. The vessel is also equipped with four 5.5 MW Wärtsilä bow thrusters, which are among the largest in the world."

Edit: Apparently on some smaller ships they did switch to CF6 engines.
https://www.cruisemapper.com/ships/Cele ... ennium-622
https://www.cruisemapper.com/wiki/752-c ... lsion-fuel

I'd imagine for the Oasis class that the fuel burn would be to much as they would need at least 4 of them.
We are all just fanboys, our opinions don't make or break businesses.

Max Q
Posts: 7857
Joined: Wed May 09, 2001 12:40 pm

### Re: The math behind twins.

Woodreau wrote:
Sure, I'll help continue the off topic divergence.

My last ship - a destroyer - had 4 gas turbine engines connected to two propellers through reduction gears. or COGAG - combined gas turbine and gas turbine.

Since the engines constantly produce "thrust" the props turned at 55 rpm whenever the engines were on which allowed the ship to travel between 0 and 12 knots. To go faster than 12 knots, increase the engine thrust by advancing the TLA levers at the control station, which could be the remote control station on the bridge, the remote control station at CCS (engineering central control station) or each of the 4 engines had their own individual local control in the main engineering space.

Sounds a lot like an Arleigh Burke DDG ?
The best contribution to safety is a competent Pilot.

Woodreau
Posts: 1825
Joined: Mon Sep 24, 2001 6:44 am

### Re: The math behind twins.

Not an Arleigh Burke, but a Spruance/Kidd.

Arleigh Burke’s engineering configuration is similar four engines two props in a COGAG arrangement but the actual performance numbers different.
Bonus animus sit, ab experientia. Quod salvatum fuerit de malis usu venit judicium.

johns624
Posts: 2321
Joined: Mon Jul 07, 2008 11:09 pm

### Re: The math behind twins.

Many warships use diesels or small gas turbines for cruising and larger gas turbines for when they need high speed.
As for locomotives, while there are D/M and D/H, the vast, vast majority are diesel-electric.

Max Q
Posts: 7857
Joined: Wed May 09, 2001 12:40 pm

### Re: The math behind twins.

Woodreau wrote:
Not an Arleigh Burke, but a Spruance/Kidd.

Arleigh Burke’s engineering configuration is similar four engines two props in a COGAG arrangement but the actual performance numbers different.

Ok

I spent a week on a ‘tiger cruise’ on the USS Milius from Pearl Harbor to San Diego when my Son was a gunner’s mate

An amazing experience, but after a week I was glad to get off

He was on the last leg of an eight month deployment, not easy, I’m sure you can relate
The best contribution to safety is a competent Pilot.

Woodreau
Posts: 1825
Joined: Mon Sep 24, 2001 6:44 am

### Re: The math behind twins.

Max Q wrote:
Ok

I spent a week on a ‘tiger cruise’ on the USS Milius from Pearl Harbor to San Diego when my Son was a gunner’s mate

An amazing experience, but after a week I was glad to get off

He was on the last leg of an eight month deployment, not easy, I’m sure you can relate

Sorry totally way off topic now

Unfortunately the tiger cruise from Hawaii to San Diego is 6 days too long. Most tigers/people are entertained for about a day/ day and a half at best. They’re usually bored the rest of the transit and can’t wait to get off the ship in San Diego.

The crew have duties to perform and it keeps them busy, so time doesn’t drag on like it does for passengers.

For example as an engineer, my life was 6 hours on, 6 hours off, standing port and starboard watches in the engineering plant. So in addition to the 12 hours of engineering watches I still had my normal 8 hours of office work to do, plus collateral duties, sleep, hygiene, PT, time to lollygag to squeeze in the remaining 12 hours.

Topside deck watches were a little easier, 4 on, 8 off or 5 on, 10 off plus the dog watches. CIC watches were 6 on 6 off. So everyday was different - different challenges - different puzzles to solve, but it was very much like Groundhog Day.

Transiting between Hawaii and San Diego is pretty boring in CIC, sometimes we’d pass the time running detect to engage drills on the airliners as they flew overhead between Hawaii and the west coast. Do the ID drill, tag it unknown assumed comair, Just about everything except assign a weapon and give the computer launch consent. We could see which planes had their weather radar on. Which manufacturer made their weather radar, etc.

Who knows what it’s like today after the recent accidents/collisions/groundings where fatigue played a major causal factor. I don’t know if they changed the watch rotations to be less fatiguing. But seeing as the newer LCS ships have less crew members to do the same amount of work and everyone has two or three jobs onboard, I doubt it.

Nothing is worse after getting back from an 8 month deployment and you tie up to the pier in homeport and everyone is lined up on the quarterdeck to depart the ship, but you can’t leave and you’re stuck on the ship for one more day because you have duty. Well maybe Its worse if you also had duty the day before the ship deployed.
Bonus animus sit, ab experientia. Quod salvatum fuerit de malis usu venit judicium.

SAAFNAV
Posts: 579
Joined: Wed Mar 17, 2010 5:41 pm

### Re: The math behind twins.

Woodreau wrote:
Topside deck watches were a little easier, 4 on, 8 off or 5 on, 10 off plus the dog watches.

I'm sorry, but I have to derail further with a Patrick O'Brien quote: Why are they called dog watches? Because they are cur-tailed.
L-382 Loadmaster; ex C-130B Navigator

Yikes!
Posts: 346
Joined: Sat Oct 13, 2001 4:51 pm

### Re: The math behind twins.

What's all this crap about boats on an AIRLINERS technical forum?????? (Just kidding! ROTFLMAO...Great discussion!)

CowAnon
Posts: 85
Joined: Fri Nov 03, 2017 12:03 am

### Re: The math behind twins.

NameOmitted wrote:
For starters, I am not questioning the math, that's been settled by people who are much more knowledgeable than myself. I am just trying to understand it.

For a twin, each engine needs to be powerful enough to operate the aircraft should the other fail, at the most vulnerable point in the flight. Each engine, therefore, needs to be rated to double the thrust for what would normally be needed. Since turbines are not nearly as efficient when they are not at near full thrust, it would seem that the engines of a twin airliner spend almost their entire operating life at an inefficient power setting. What am I missing?

I'm in a similar position, and I'm glad you brought up these questions. I also am curious about how you size the engines if you needed to convert a twin-engine airplane into a four-holer. (No comments about whether you think that's a good idea, please.)

I've read that turbofans are sized for takeoff thrust, which means they would have excess thrust at cruise. Suppose you wanted to convert an A359, which is near the sweet spot of the current widebody market. Since each Trent XWB engine has about 84,000 pounds of takeoff thrust, you could theoretically size each engine for a takeoff thrust of ( 84,000 pounds / (4 engines - 1 engine out) ) = 28,000 pounds. This 28k# engine thrust rating is right in the middle of the thrust range for the best selling engines in the entire airplane market, the LEAP and the GTF, so you could benefit from the economy of scale of their unit productions. However, for the 99.99x% of the time you don't have an engine out, the total airplane takeoff thrust is (4 * 28,000) = 112k# for the quad airliner vs. (2 * 84,000) = 168k# for the twin airliner. If the ratio of cruise thrust to takeoff thrust is the same for both engine sizes, you only get (112,000 / 168,000) = 2/3 of the cruise thrust for a quad airliner compared to the twin airliner. Which would be fine if the excess thrust at cruise for the turbofan is at least 1 / (2/3) = 1.5, meaning 50% higher than the required cruise. What is the typical excess thrust ratio in cruise, anyway? 50% higher seems pretty wasteful.

On the other hand, if you simply match the plane's total takeoff thrust when fiddling with the number of engines without accounting for engine-out, you get (168,000 pounds / 4 engines) = 42k# per quad engine, which is in the no-man's land of thrust ratings for the current airplane engine market. Also, you now have ( (4 engines - 1 engine out) * (42,000 pounds) ) = 126,000 pounds of takeoff thrust, which is much more than the 84,000 pounds you need, and you would still have the same amount excess thrust capability during cruise as for the twin airliner. So is there a simple rule of thumb for sizing a four-engine airplane other than the (flawed) methods I've mentioned?

GalaxyFlyer
Posts: 4129
Joined: Fri Jan 01, 2016 4:44 am

### Re: The math behind twins.

Since your question requires “all else being equal” which is never the case, the answer is there is no simple rule of thumb. The nearest plane would be the A330/A340 design.

Starlionblue
Posts: 19497
Joined: Fri Feb 27, 2004 9:54 pm

### Re: The math behind twins.

CowAnon wrote:
NameOmitted wrote:
For starters, I am not questioning the math, that's been settled by people who are much more knowledgeable than myself. I am just trying to understand it.

For a twin, each engine needs to be powerful enough to operate the aircraft should the other fail, at the most vulnerable point in the flight. Each engine, therefore, needs to be rated to double the thrust for what would normally be needed. Since turbines are not nearly as efficient when they are not at near full thrust, it would seem that the engines of a twin airliner spend almost their entire operating life at an inefficient power setting. What am I missing?

I'm in a similar position, and I'm glad you brought up these questions. I also am curious about how you size the engines if you needed to convert a twin-engine airplane into a four-holer. (No comments about whether you think that's a good idea, please.)

I've read that turbofans are sized for takeoff thrust, which means they would have excess thrust at cruise. Suppose you wanted to convert an A359, which is near the sweet spot of the current widebody market. Since each Trent XWB engine has about 84,000 pounds of takeoff thrust, you could theoretically size each engine for a takeoff thrust of ( 84,000 pounds / (4 engines - 1 engine out) ) = 28,000 pounds. This 28k# engine thrust rating is right in the middle of the thrust range for the best selling engines in the entire airplane market, the LEAP and the GTF, so you could benefit from the economy of scale of their unit productions. However, for the 99.99x% of the time you don't have an engine out, the total airplane takeoff thrust is (4 * 28,000) = 112k# for the quad airliner vs. (2 * 84,000) = 168k# for the twin airliner. If the ratio of cruise thrust to takeoff thrust is the same for both engine sizes, you only get (112,000 / 168,000) = 2/3 of the cruise thrust for a quad airliner compared to the twin airliner. Which would be fine if the excess thrust at cruise for the turbofan is at least 1 / (2/3) = 1.5, meaning 50% higher than the required cruise. What is the typical excess thrust ratio in cruise, anyway? 50% higher seems pretty wasteful.

On the other hand, if you simply match the plane's total takeoff thrust when fiddling with the number of engines without accounting for engine-out, you get (168,000 pounds / 4 engines) = 42k# per quad engine, which is in the no-man's land of thrust ratings for the current airplane engine market. Also, you now have ( (4 engines - 1 engine out) * (42,000 pounds) ) = 126,000 pounds of takeoff thrust, which is much more than the 84,000 pounds you need, and you would still have the same amount excess thrust capability during cruise as for the twin airliner. So is there a simple rule of thumb for sizing a four-engine airplane other than the (flawed) methods I've mentioned?

Again, there is very little "excess" thrust in cruise. As I said upthread, the much lower air density means much lower thrust at altitude despite running at around 80-85% of maximum N1. The typically available thrust in cruise is significantly less than 10%, assuming you're at your optimum level. Going from cruise power to MCT or even TOGA makes barely any difference.

This is valid for twins or quads. Any "excess" thrust will simply be used to carry more or fly higher. You're not going to be flying around with massive margins in the cruise.

I'm not an aircraft designer, but I imagine more goes into it than simply the amount of takeoff thrust. The engines will be adapted to the specific airframe, especially the wing. The Trent XWB-84 and XWB-97 are practically the same engine, except one puts out 13000 more lb/ft because the A350-1000 is heavier than the A350-900.
"There are no stupid questions, but there are a lot of inquisitive idiots." - John Ringo

GalaxyFlyer
Posts: 4129
Joined: Fri Jan 01, 2016 4:44 am

### Re: The math behind twins.

This was offered to me by a Boeing propulsion engineer several years ago.

If you look at a plot of TSFC for a typical turbofan engine (specific fuel consumption on the vertical scale, thrust on the horizontal) it looks rather like a stretched out 'U'. At very low power and very high power, the efficiency is fairly poor, but it's really good in the middle. This is 'OK' because you're still not burning much fuel at idle, and you don't spend more than a few minutes per flight at takeoff. The efficiency at idle is so poor that for some engine types, as you accelerate from minimum ground idle to flight or approach idle, the EGT actually drops. Now this 'U' curve moves around with altitude, airspeed, and total temp (it's mainly a function of inlet total pressure) but the basic shape remains.

Now this is a broad generalization, but because twins are overpowered relative to quads they tend to cruise closer to the bottom of that 'U' shaped TSFC curve while a quad tends to move more up the increasing TSFC slope due to the higher relative thrust demand.

As an extreme example, think of the case of a 747 with an engine out. Now, a 747-400 or -8 will happily cruise on 3 engines at 35k or above provided it's not really heavy. But the fuel consumption skyrockets relative to 4 engine cruise because now you're way up on the high power side of that U curve.

GF

gloom
Posts: 347
Joined: Thu Jun 30, 2016 4:24 pm

### Re: The math behind twins.

SInce we are at this, let me share my thoughts.

There are three critical considerations there.

1. Takeoff run. You can safely assumed it's always at maximum aircraft power (in terms of both engines running, and highest spool speeds), and it's (due to quite low drag at these speeds) mostly dependant on thrust to weight ratio. You want an airliner to be able to accelerate so it departs as soon as practical. This is quite often limiting, given the wing area (lower or higher takeoff speed).
2. Departure phase - assuming plane made it to departure, it needs to climb quick enough to clear all obstacles. This is called required climb gradient, and is airport/departure specific. Dince you can't stop departure after v1, plane needs to be able to meet climb gradient without one engine, so twin needs to achieve this on one engine, quad needs to achieve it with three. That's where quads are better. Howevery, usually climb gradient is more of a problem on airports where it's either high, hot, or both. That's why some airlines tended to go with A340 for long distance flights rather, than 777.
3. Cruise phase - this is where fun part begins. Engines at this altitude are producing around 20% of takeoff thrust, but also the drag is much lower at altitude. However, excess of thrust is quite low, around 10-20% of net thrust at max cruise thrust. That's why if an engine fails, the plane will be descended and also the speed reduced. Usually, conditions for such thrust are part of airplane manuals.

Basically, you could assume quads are usually takeoff limited, twins are climb gradient limited. For long range planes, development of engines starting in 80s (CF6 was the first big engine with good reliability I think, followed by 777s GE90) is what made LR twins possible and viable options.

Just my 2c.

Cheers,
Adam

Starlionblue
Posts: 19497
Joined: Fri Feb 27, 2004 9:54 pm

### Re: The math behind twins.

gloom wrote:
SInce we are at this, let me share my thoughts.

There are three critical considerations there.

1. Takeoff run. You can safely assumed it's always at maximum aircraft power (in terms of both engines running, and highest spool speeds), and it's (due to quite low drag at these speeds) mostly dependant on thrust to weight ratio. You want an airliner to be able to accelerate so it departs as soon as practical. This is quite often limiting, given the wing area (lower or higher takeoff speed).
2. Departure phase - assuming plane made it to departure, it needs to climb quick enough to clear all obstacles. This is called required climb gradient, and is airport/departure specific. Dince you can't stop departure after v1, plane needs to be able to meet climb gradient without one engine, so twin needs to achieve this on one engine, quad needs to achieve it with three. That's where quads are better. Howevery, usually climb gradient is more of a problem on airports where it's either high, hot, or both. That's why some airlines tended to go with A340 for long distance flights rather, than 777.
3. Cruise phase - this is where fun part begins. Engines at this altitude are producing around 20% of takeoff thrust, but also the drag is much lower at altitude. However, excess of thrust is quite low, around 10-20% of net thrust at max cruise thrust. That's why if an engine fails, the plane will be descended and also the speed reduced. Usually, conditions for such thrust are part of airplane manuals.

Basically, you could assume quads are usually takeoff limited, twins are climb gradient limited. For long range planes, development of engines starting in 80s (CF6 was the first big engine with good reliability I think, followed by 777s GE90) is what made LR twins possible and viable options.

Just my 2c.

Cheers,
Adam

You are incorrect in your assumptions about max power.

1. Takeoff run. The vast majority of takeoffs are done with reduced thrust, normally flex/assumed temp. The savings in terms of reduced engine wear far outweigh the additional fuel burn. Most runways are long enough for the mission and the conditions on the day, so there is no need for TOGA. Even on long haul and ultra long haul, reduced thrust is typically used.

2. Departure phase. Again, climb thrust is typically derated. And again, the savings in terms of reduced engine wear far outweigh the additional fuel burn. Obstacles are sometimes a consideration, and sometimes ATC restrictions like "level by the FIR boundary". But derate can be used more often than not. To paraphrase our company policy, if ATC wants you to climb faster, first you negotiate, then you decelerate, and only if neither of those is enough do you take out the derate. Hence the mantra, "Negotiate, decelerate, derate."
"There are no stupid questions, but there are a lot of inquisitive idiots." - John Ringo

gloom
Posts: 347
Joined: Thu Jun 30, 2016 4:24 pm

### Re: The math behind twins.

Starlionblue wrote:
You are incorrect in your assumptions about max power.

Starlionblue - I know about derates and how much of "real max" it takes.

Still, it's a max for engines on a given flight. If you look for spool rotations, they're most stressed on takeoff, even if derated. Transition from takeoff to climb, and from climb to cruise are always down (lower rotations, lower thrust), even on derated takeoffs/climbs. And this is what I used that for. Perhaps I should've used other word, so it's clear it's not "absolute max power", only "relational max power".

Cheers,
Adam

GalaxyFlyer
Posts: 4129
Joined: Fri Jan 01, 2016 4:44 am

### Re: The math behind twins.

Depends if you’re talking about certification at MTOGW, necessarily the manufacturer is going to try to demonstrate max payload or max range. Operationally, the norm is reduced or derated thrust, as appropriate for payload/range. Certification will always be bounded by the rules for climb case OEI for twins, often by 115% of AEO take-off ground run. Next requirement is thrust at the wing’s optimum altitude, especially for quads. See optimum altitudes flown by early 747s, thrust-limited in the high 20s.

Starlionblue
Posts: 19497
Joined: Fri Feb 27, 2004 9:54 pm

### Re: The math behind twins.

gloom wrote:
Starlionblue wrote:
You are incorrect in your assumptions about max power.

Starlionblue - I know about derates and how much of "real max" it takes.

Still, it's a max for engines on a given flight. If you look for spool rotations, they're most stressed on takeoff, even if derated. Transition from takeoff to climb, and from climb to cruise are always down (lower rotations, lower thrust), even on derated takeoffs/climbs. And this is what I used that for. Perhaps I should've used other word, so it's clear it's not "absolute max power", only "relational max power".

Cheers,
Adam

Thx for clarifying.

AFAIK you can in some cases have an increase in thrust when going from takeoff to climb power if you're using a fixed derate due to a contaminated runway.
"There are no stupid questions, but there are a lot of inquisitive idiots." - John Ringo

kitplane01
Posts: 1372
Joined: Thu Jun 16, 2016 5:58 am

### Re: The math behind twins.

Woodreau wrote:
NameOmitted wrote:
So, to be clear, you are telling us that she would do 12 knots while essentially at idle?

Is that with one of her plants running?

Leaving and entering port, all 4 engines will be online and the electrical network split unless there is some engineering casualty which prevents all 4 engines being online.
with all 4 engines at idle at 100% pitch, the ship will do 12 knots.

To go slower, the blade pitch will be reduced - with the ship tied up alongside the pier when engineering is ready to answer bells, prior to taking in all lines and getting underway the props will be turning 55rpm at 0 pitch.

Weird. Does the ship not have clutches between the shaft and the turbine? I would think that would help a million different ways, including start up and maintenance, and running one engine with the other stopped.

Love the ship stories. Need more!!

aklrno
Posts: 1533
Joined: Sat Dec 04, 2010 11:18 pm

### Re: The math behind twins.

Going back to the original question, the issue is efficiency. There are multiple ways to measure efficiency. If it is power/kg of engine mass to be lifted, then running at half power means half efficiency. If it is fuel efficiency, isn't the issue more about the temperature difference between the hot end and the cold end of the thermodynamic cycle? You could be at half power and still be getting full fuel efficiency if you maximize the Carnot cycle efficiency which is just temperature dependent.

gloom
Posts: 347
Joined: Thu Jun 30, 2016 4:24 pm

### Re: The math behind twins.

kitplane01 wrote:
Weird. Does the ship not have clutches between the shaft and the turbine?

For this magnitude of power, it's way easier to use constant propeller speed and pitch control, just the way the planes do. Clutch would have to be extremely large, and the problems related to power (temperatures, potential slip, power to engage/disengage, even transfer efficiency) work against it.

Cheers,
Adam

Woodreau
Posts: 1825
Joined: Mon Sep 24, 2001 6:44 am

### Re: The math behind twins.

There is a clutch between the prime mover (gas turbine engine) and the main engine (reduction gears) but not between the main engine and the propeller shaft.

Since there are two gas turbine engines for each shaft, having a clutch allows one gas turbine engine to be secured for whatever reason.

If there isn’t a need for all engines to be online, i.e., steady state transit, a typical configuration would be to secure three engines leaving one engine to drive a propeller shaft, and the other propeller shaft trailed - it just free spins due to hydrodynamic pressure.

Throughout the lifetime of the ship, the propeller shaft is never stopped. It will always have some rotation in order to prevent bowing of the shaft. In port with all engines secured, the propeller shaft will still be turning at 6 rph. (Rotations per hour)
Bonus animus sit, ab experientia. Quod salvatum fuerit de malis usu venit judicium.

NameOmitted
Topic Author
Posts: 722
Joined: Sun Oct 23, 2016 7:59 pm

### Re: The math behind twins.

Woodreau wrote:
In port with all engines secured, the propeller shaft will still be turning at 6 rph. (Rotations per hour)

What is rotating the shaft with the engines secured?

Woodreau
Posts: 1825
Joined: Mon Sep 24, 2001 6:44 am

### Re: The math behind twins.

There is a jacking gear, an electric motor, that will rotate the main engine which turns the propeller shaft.
Bonus animus sit, ab experientia. Quod salvatum fuerit de malis usu venit judicium.

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