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I Minute physics video: Why Are Airplane Engines So Big?

  1. Jul 26, 2017 #1


    The video shows some optimisations on the turbofan engine and reaches the conclusion it needs to be about 4m.
    The premise is that accelerating more air a little is more efficient than accelerating less air to a higher acceleration and speed, fact mentioned in all aerodynamics books, and that "bigger" creates more drag, fact that seems valid but I cold not find any reference of propeller diameter vs. drag.
    Could anybody walk me through the math presented? I have a hard time understanding it.
     
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  3. Jul 26, 2017 #2

    jedishrfu

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    Well here's a reference for boat propellers and drag:

    http://www.ribadventure.gr/index.ph...llers-diameter-en&catid=39&Itemid=256&lang=en

    and this more technical treatment from MIT:

    http://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node86.html

    11.7.3 talks about thrust equaling drag for level flight

     
  4. Jul 27, 2017 #3
    Thank you jedishrfu,

    I got some more info on this. The propeller blades act as airfoils, lift and drag acting as thrust and torque, respectively. One would want to drive the propeller at a optimum L/D ratio, generally alpha at about 5 deg as exemplified by Clark Y airfoil characteristics ( http://airfoiltools.com/airfoil/details?airfoil=clarky-il, see cl/cd vs alpha graph)
    For a specific thrust to be generated, at optimum L/D, the blade geometry is set, the blade length and chord need to have certain dimensions, the prop having a certain diameter.
    Having a bigger propeller giving similar thrust, it needs to be driven at a lower alpha, getting smaller L/D than optimum, meaning you need more torque and power, expending more energy that the optimum case.
    All this is not considering that a bigger propeller is having higher wetted area and you loose energy that way too.
     
  5. Jul 27, 2017 #4

    Nidum

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    There is no one single ideal diameter for the fans in turbofan engines .

    The diameter is determined as part of the complex design optimisation process for a particular engine and the specific application the engine is intended for .

    The fan designs used in modern turbo fans have little in common with traditional simple propeller designs .

    Practical maximum diameter of the fan is usually determined by stress levels and other mechanical considerations .

    With the usual design of turbofan having the fan located at the leading end of the engine the central part of the fan forms the first compressor stage for the core engine .

    RR TRENT1000
     
    Last edited: Jul 28, 2017
  6. Jul 30, 2017 #5

    David Lewis

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    The bigger prop will give more thrust for a given power input. In any case, you want the blade airfoil to operate at its max L/D angle of attack.

    The performance parameter you are discussing is propeller disc loading (thrust/prop disc area). As loading goes down, efficiency goes up, assuming optimum design. The exception is airplanes going very fast. The large diameter may cause the blade tips to operate at transonic speeds, which hurts efficiency.
     
  7. Jul 30, 2017 #6

    russ_watters

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    You're barking up the wrong tree here with this drag issue. The reason fans need to be as big as possible is the bigger the fan the lower the power needed to generate the thrust.

    Fans generate thrust with a change in momentum: mv. But they burn power based on the imparted kinetic energy; .5mv2. Since you can generate more force with a larger m or a larger v, mimimizing the kinetic energy added means using a larger m and lower v.
     
  8. Jul 30, 2017 #7

    David Lewis

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    When the airplane is moving slowly, such as during takeoff, low disc loading is especially important. A higher speeds the benefit is smaller.
     
  9. Jul 31, 2017 #8
    So far as i got the bigger the better, in theory, or at slow speeds, and I totally got this; and it makes sense, lower kinetic energy and low disk loading.
    But at higher speed, a bigger propeller will have actually have a higher drag than a smaller propeller, and excluding the transonic tip speed. The cause of it being the parasitic drag being much higher than induced drag at high speed, and considering blades behaving like wings, the parasitic drag is exemplified in this graph: https://en.wikipedia.org/wiki/Parasitic_drag#/media/File:Drag_curves_for_aircraft_in_flight.svg
    One would want a prop having such a diameter to have enough thrust for accelerating the plane for a reasonable takeof distance, but not as big to have an excessive drag at higher speed.
     
  10. Jul 31, 2017 #9

    russ_watters

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    But a small propeller has to rotate faster than a big propeller, not slower. For that reason, the smaller propeller would generate more drag, not less.
     
  11. Jul 31, 2017 #10
    @watters: A smaller propeller would need to rotate faster, but the tips speed would be the same; the bigger propeller having more surface spinning faster, so having more friction.
     
  12. Jul 31, 2017 #11

    russ_watters

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    That isn't true; it has to produce a higher airflow velocity, so it must either have a higher pitch (and therefore produce more drag) or higher velocity (and therefore produce more drag).
    The linear/square relationship still applies: since drag is a function of velocity squared, moving less air faster produces more drag than moving more air slower.

    You might try looking at some real fan performance:
    http://www.tcf.com/docs/product-bul...eaxial-fans---catalog-ax100.pdf?Status=Master

    The difference isn't substantial, but you will find that the efficiency of these fans goes up, not down, when you increase the fan size.
     
    Last edited: Jul 31, 2017
  13. Jul 31, 2017 #12
    As presented here: http://www.jefflewis.net/aviation_theory-theo_prop_eff.html, two propellers, one of 8ft and another 16ft are generating similar theoretical thrust above a certain forward speed (see the last graph), calculated for same input power, but without taking into consideration the parasitic drag which would be much higher for the bigger propeller.
     
  14. Jul 31, 2017 #13

    russ_watters

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    Neither of those bolded statements are true. In a separate graph, it shows how input power goes down - radically - the larger a propeller is, for the same thrust. Applied to the graph you were referring to, it means for all of those points, the larger propeller produces that shown thrust at a much lower input power than the smaller fan.

    From the link I provided above, you can look at some actual fan performance and see the same thing:

    18" fan at 0.5" S.P. and 9,000 CFM: 4.75 hp, 5000 fpm. That's 29 lb of thrust.

    For a 36" fan (4x the area) producing the same thrust takes twice the airflow (volumetric) at 1/2 the velocity. So that is 18,000 CFM at 3.26 hp. (Back check: 18000/13.2/32.2/3600*2512=29.6 lb thrust). Because of the increased efficiency of the bigger fan, that 3.26 hp input is actually less than what is predicted by the theory, which is 3.36 hp.
     
  15. Jul 31, 2017 #14
    What you are saying is true for statically produced thrust, your link presents axial fans for ventilation, not really suited for aircraft.
    At higher speed, the propeller diameter starts to be less important, same input power theoretically generating same amount of thrust.
    Propeller efficiency:
    frm_effi.gif
    so thrust is dependent of efficiency, power and speed, it has nothing to do with the diameter, theoretically.
    So it would make sense to have same trust for the same power expended, but when you consider the loses cased by parasitic drag, you reach the conclusion that above a certain speed a smaller propeller will be practically more efficient.
    The same thing is presented into this graph:
    aviation_theory-thrust_vs_airspeed-2_dia.gif
    Above 150mph, almost the same thrust is generated by both propellers at same power.
     
    Last edited: Jul 31, 2017
  16. Jul 31, 2017 #15

    FactChecker

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    Momentum is proportional to V (p = m*V) and energy is proportional to V2 (e = 0.5*m*V2), so a low velocity gives more momentum for a given amount of energy. To propel an airplane efficiently, you want to move a greater air mass at a smaller velocity.

    Of course there are a lot of other things to consider, but that is the basic advantage of larger fans.
     
    Last edited: Jul 31, 2017
  17. Jul 31, 2017 #16

    russ_watters

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    Ehem: the speed of the air from the fan is inversely proportional to its diameter, for the same thrust. You are ignoring it, but it is in there.

    If what you are saying were true, helicopters would have smaller blades and jets would have smaller bypass fans.
    Now you are doubling-down on the wrong: even if the previous thing you said were true, that still would not be.

    I'm going to be more demanding of rigor:
    Please quote where it says they are at the same power.
     
  18. Jul 31, 2017 #17
    The speed in the efficiency calculation is not the speed of air induced by the fan, but the speed of the aircraft trough the air.

    It is right there in the quoted paper:"For the same horsepower, the amount of static thrust that you can produce just keeps going up with diameter. This increased thrust won't be nearly so marked throughout the whole flight, however, as the second chart below illustrates. It can be seen that even with diameters different by a factor of 2, both propellers produced nearly the same thrust at 200 mph"
    And also on the graph: "400HP"
     
  19. Jul 31, 2017 #18
    Helicopters have indeed big rotors, and only because they need to have a lot of thrust for the static condition, when they are hovering, to increase figure of merit. Those big rotors are also an impediment for attaining high speeds, as drag increases, forward speed creating asymmetry of lift and ultimate retreating blade stall.
     
  20. Jul 31, 2017 #19

    russ_watters

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    You're right, I tripped over that, and I apologize. But as for what it means, I'll circle back to it...
    Right again. I deal with fans every day and since they don't move, the only relevant speed is the speed of the air across the fan. Still, the difference explains the graph above: It's the reason for the convergence in the graph: as the aircraft gets faster, the aircraft's speed is a larger and larger fraction of the total speed across the fan, which reduces the benefit of the larger fan.

    One thing about the equation in the video though: the drag coefficient is an assumption and a constant, not a variable with fan diameter. That means that the optimization is occurring without considering that the drag coefficient could increase with propeller diameter.
     
    Last edited: Jul 31, 2017
  21. Jul 31, 2017 #20

    FactChecker

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    I see that the basic trade-off between air velocity versus air mass flow is well presented in the video and well understood. I can not fully figure out the equations in the video. I think that the main drag effect that I don't see mentioned yet is simply due to the greater weight of a larger engine requiring greater wing lift and therefore greater drag.
     
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