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  • Optimising miles per litre

    We all know (don't we) that if gliding into wind it's necessary to increase speed beyond min sink speed to get the best range. There are relatively easy techniques to work out this best speed given a fairly elementary knowledge of the aircraft's glide performance.

    Now say I want to fly an enroute leg into a significant headwind, how can I work out the best speed to fly (or RPM to use) to minimise my fuel consumption over the distance to be covered (or maximise the distance I can cover with the fuel I have in the tank). Assuming I haven't got a fuel flow gauge.

    I know there are performance graphs in the rotax operators manuals but they are encoded in engineering terms rather than operator terms - eg fuel flow vs rpm is in g/kWh.

    This is surely a problem solved quite often by the competition pilots in their limited-fuel events, so any guidance out there? rules of thumb? help?

    Last edited by Joan Walsh; 25th March 2018, 14:37. Reason: clarification
    The pilot formerly posting as MadamBreakneck
    R examiner and TST pilot.
    and now a Tai Chi instructor

  • #2
    Fly slowly! It may seem odd advice, but most of our planes are set up to fly faster than best glide speed, which is also the most efficient cruise speed (to a reasonable approximation).

    You need to speed up a little against a headwind, but its surprisingly little - for a traditional trike it was around half the headwind if I remember correctly, from some measurements many years ago. So even a 20mph headwind would still be flown at only ~50mph. Quite counter-intuitive when you are trying to push back up wind towards home with a dwindling fuel load.

    More modern, faster machines can push a bit harder above their best glide without much fuel cost.

    To work it out properly you need to do some tank filling and draining and get your fuel burn vs speed to work with.

    Cheers,
    Paul.

    Comment


    • #3
      Sounds like one needs to do a mpg curve for your chose flying machine in 'still air' at several speeds within its normal operating range, and another for miles covered per hour at these speeds against rising wind speeds - using headwind component. If I wasn't so idle I'd draw up some dummy curves to see how to use them in combination.

      However, with fuel consumption in the 912 Rans of 12 to 17 L/h and normal 98 mph some 14 l/h one's usually dawdling for fun or trying to get somewhere & only thinking of time en route yet not so profligate as to waste time having to stop for fuel.

      Surely in over 100 years this has been resolved multiple times.

      mikehallam.

      Comment


      • #4
        Mmm well I always go to Langeweische's Stick and Rudder for practical advice on questions like these. P 356 How to Stretch Your Fuel against a Wind. Basically he says
        1. The data you need are hard to get and the calculations very intricate, and
        2. The influence of wind on best speed is much less than you'd think. Example: best range speed in still air 75kn, then in 10kn headwind best speed is 77kn.
        So don't worry about it, in summary. But, very definitely, don't increase your speed in an attempt to push through the wind.

        Intuitively this seems different to the case in gliding where you are trying to make headway with a minimum height loss and the polar diagram can tell you exactly what speed to fly - gliders have crude 'speed to fly' rings on their varos and more sophisticated ones have electronic computers to tell you which, being linked to the GPS, vario, and asi, can work it all out for you
        Martin Watson
        Microlights in Norfolk
        Fixed Wing Instruction - Exams and GSTs - Revalidations
        07805 716407

        Comment


        • #5
          Ah yes, but... lets take an extreme case, but not ridiculously so, to illustrate my point. When the headwind is a small proportion of my airspeed (let's not fret about IAS/CAS/TAS convertions and assume for the argument that they are all the same as each other) then the difference is also small and beyond my ability to fly accurately enough for the effect to make a difference.

          However, take the TST that is once again my usual mount. On a bimble, I'd usually set a lowish rpm and cruise at about 45kt, but say I wanted to get back to the airfield and realised I'd been suckered into wandering downwind in a 25kt upper wind*. In that case my groundspeed home would be 20 knots, less than half my airspeed: my fuel burn per mile would be more than double the still air level. If I were to add a moderate increase to my airspeed of say 10 knots, it would add 50% to my groundspeed: now would that speed increase also add 50% to my fuel flow. If it did, or more, then slow and sure is indeed the answer but if not, then there would be a fuel consumption advantage in speeding up?

          Martin, don't forget that the MacCready Ring indicates an optimum airspeed to minimise height loss for a glider flying through sink between thermals and is based on the pilots estimate of the average climb rate in the next usable thermal. I'll agree that slowing down in lift and speeding up in sink is a viable method for economising fuel burn in microlights - in fact I think Cosgrove makes some mention. It's a thought though: would the gliding (or engine idle) polar curve for a microlight act as an surrogate for for fuel burn rate within a practical range of speeds?

          Thoughts?

          Joan
          * been there, done that - more than once! and yes, I did drop to lower altitude in hope of getting a less enthusiastic headwind, and I also added
          The pilot formerly posting as MadamBreakneck
          R examiner and TST pilot.
          and now a Tai Chi instructor

          Comment


          • #6
            Originally posted by Joan Walsh View Post
            We all know (don't we) that if gliding into wind it's necessary to increase speed beyond min sink speed to get the best range.
            You don't use min sink for anything involving efficiency IMV, you use best glide. Even with a tail wind it's unlikely you slow down to min sink, although you'd get close.

            Take the polar curve for the aircraft in question, you need two points for a rough quadratic, you've got min sink and max glide, use those two.

            Originally posted by Joan Walsh View Post
            It's a thought though: would the gliding (or engine idle) polar curve for a microlight act as an surrogate for for fuel burn rate within a practical range of speeds?

            Thoughts?

            Joan
            * been there, done that - more than once! and yes, I did drop to lower altitude in hope of getting a less enthusiastic headwind, and I also added
            With your polar curve, in nil wind you draw a from the origin to kiss the polar curve tangentially. The speed at which the tangent touches is your best glide speed, the angle the line makes is your best glide angle, if the axes are the same scales, if not simply divide speed by sink rate at the speed to get the glide ratio.

            Now, for best glide in head or tail wing you move the point at which the tangent crosses the X-axis to represent the head wind or tail wind, again, have it touch your polar tangentially, then that again gives you the new speed to fly at that head wind setting, and the glide angle for that head wind.

            That way you always fly at the best glide particular speed for that , which by definition is the most efficient, which by definition uses the least fuel.

            Eye thang ewe. Someone who remembers the aerodynamic theory can now confuse me with the differences between cruise at constant speed, constant altitude and constant Cl (co-efficient of lift). All have subtle differences.

            Comment


            • #7
              Just for fun & from poor memory I did some rough calc's for the Rans miles per litre at headwinds from 0 to 30 in 10 mph steps.
              Clearly at higher winds unless you crack on you stand still and mpg approaches infinity !


              However without my precise figures to hand the rough calculations on the back of an envelope suggest increase air speed by 3/4 of head wind at most usable Rans speeds for best miles/litre - as well as best sensible point to point speed.

              mike hallam

              Comment


              • #8
                From first principles:
                Parasistic drag increases with the square of airspeed.
                Induced drag also increases with the square of airspeed, but so does the lift it generates. Thus as the aircraft is trimmed for higher speed, to maintain the same lift, there is no increase in induced drag.
                For the purposes of a TST, within the normal range of speeds, we might reasonably approximate that virtually all of the drag is parasitic, so the power/speed relationship is square law (i.e. to double the speed requires four times the power, so the efficiency is halved).
                This shows that in still air, lower flying speed will give higher efficiency (within the normal speed range - anywhere close to stall and the above assumptions fall apart).
                Now, if we put the aircraft into a headwind, the relationship between ground speed and efficiency is altered.
                With a 30kt wind and 45kt airspeed, ground speed is 15kt. Increase airspeed to 60kt and efficiency might fall to approximately 2/3 what it was at 45kt.
                However, ground speed has increased to 30kt, so the trip time will be reduced to 1/2 of what it would have been at 45kt airspeed. Running at 2/3 efficiency for half the time uses 25% less fuel.
                Pete T.

                "A closed mouth gathers no feet".

                Comment


                • #9
                  Drag to speed is a square law, but the power required = drag x speed, so that's a cube law (Power~speed ^ 3). So its much worse than you think!

                  Comment


                  • #10
                    And the fuel consumed by the engine at anything other than optimal rpm and power is worse. The 582 frinstance is awful anywhere away from about 5000rpm. Any attempt to fly at a higher power setting crucified the fuel consumption.
                    Our wings are a bit like boat hulls - they are designed to be efficient at one particular air speed. Try to go faster and the extra power needed is counterproductive.
                    I come back to what Langeweische's book says - go a tiny bit faster into a headwind, but no more.
                    Martin Watson
                    Microlights in Norfolk
                    Fixed Wing Instruction - Exams and GSTs - Revalidations
                    07805 716407

                    Comment


                    • #11
                      Bill Brooks has done quite a bit of long distance stuff on the HypeR, and with a 30 mph headwind it's worth his while flying flat out at about 90-something mph.

                      OK, so he's 912S is that, but as soon as you start backing away from the ideal speed to fly, time in the air really goes up.

                      With regard to the 582, in something like an X-Air Falcon, you have to be up at 5,300-ish to maintain height at best glide, about 51 knots. So it drinks fuel anyway.

                      I could spreadsheet it, but the numbers may not win the argument...

                      Comment


                      • #12
                        This could be gibberish and I've got something else to do later so I haven't time to think it through, but thus far...

                        I bunged the Rotax 503 data from the manual into a spreadsheet, but the fuel flow (litres per hour) curve counter-intuitively flattened out with increasing rpm. This is a result of the energy conversion efficiency improving with power demand (the grams per kilowatt hour vs rpm curve). Deciding that the curves must have been generated by load with a dynamometer, I put in a semi-arbitrary square law 'drag factor' based on rpm squared and a fiddle-factor constant which gave the fuel flow curve a more believable shape, rising faster with higher rpm. Then bingo! following FPW's post I changed the drag factor' to a cube law - this has resulted in a curve which sort-of matches a mix of empirical and anecdotal figures for a 503. See atached.
                        Now all I need to do is fly experimentally and set up two curves (1-up and 2-up) of level flight speed at a set of rpms over the practical range for my aeroplane; and from that I can derive a pair of fuel flow per knot curves from which I can get as near as matters an answer to my original question... I think.

                        503 graphs.jpg
                        The pilot formerly posting as MadamBreakneck
                        R examiner and TST pilot.
                        and now a Tai Chi instructor

                        Comment


                        • #13
                          What's the vertical scale pls ?

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                          • #14
                            Originally posted by mikehallam View Post
                            What's the vertical scale pls ?
                            Non-dimensional. Use description of line, such as mililitres per hour, or power in watts - a bit odd I know but its the way the numbers worked out for graphing in the same space

                            At least it looks daft enough that it might inhibit the graph from wandering the net gaining some sort of unwarranted cred by repetition

                            The lines Power (in Watts) and Fuel (in grams per kilowatt.hour) are from the Rotax charts. The rest are derived by M$magic assuming a constant petrol density of 0.72 grams per mililitre. The line Flight (in mililitres per hour) is derived from Flow (in mililitres per hour) multiplied by cube of RPM and an arbitrary constant to make the numbers look plausible... all the scientific rigour of a tabloid astrology column.

                            Hope that helps.
                            Last edited by Joan Walsh; 29th March 2018, 15:48. Reason: slight clarification
                            The pilot formerly posting as MadamBreakneck
                            R examiner and TST pilot.
                            and now a Tai Chi instructor

                            Comment


                            • #15
                              We'll, ok, but
                              Aren't the figures/graphs of fuel consumption Vs rpm based on wide open throttle? I mean they are to help with selection of gear ratios and prop pitch design?
                              In which case they don't help here.
                              Maybe I've misunderstood, but I think it's even more complicated than we've said so far.
                              For example, what happens at different weights? How do we account for that?
                              Martin Watson
                              Microlights in Norfolk
                              Fixed Wing Instruction - Exams and GSTs - Revalidations
                              07805 716407

                              Comment

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