RE: [Flightgear-devel] Spitfire Propeller vs. YASim
> -Original Message- > From: Vivian Meazza > Sent: 04 May 2004 7:38 pm > To: 'FlightGear developers discussions' > Subject: RE: [Flightgear-devel] Spitfire Propeller vs. YASim > > Richard Bytheway wrote > > > Sent: 04 May 2004 10:42 > > To: FlightGear developers discussions > > Subject: RE: [Flightgear-devel] Spitfire Propeller vs. YASim > > > > > > > I had already shown by some pretty simple math that at 2850 > > > rmp the tips of > > > a 1.65m radius propeller would be supersonic and therefore highly > > > improbable, but we now know that the data of hp, gear ratio, > > > rpm etc all tie > > > together. > > > > > > Thanks > > > > > > Vivian Meazza > > > > > > > I have a memory from years back of being told that the reason > > the Spitfire had such a distinctive sound was that the > > propellor tips _were_ supersonic. Maybe it was just heresay. > > > > Richard > > > > I think it is possible that the propeller tips went supersonic in the > corners of the flight envelope of some of the later versions. > However, the > math seems to show that in most circumstances they were not. It seems > unlikely that this could explain the distinctive sound when > heard from the > ground. > > Here are some calculations on propeller rpm. > > The propeller the tip speed should be as high as possible > with the only > limitation being that the tip should not get into the region > of aerodynamic > compressibility. Typically a figure of Mach 0.85 is used as > the magic number > that should not be exceeded. (This makes some allowance for the speed > increase as the air passes over the aerofoil curved surface > and the increase > in air velocity caused by the propeller operation.) > > If we take 8000 ft as the operating altitude then Mach 1 = > 1085 ft/sec > (approx) > > Assuming that the forward velocity of the aircraft is 300 mph > = 440 ft/sec > > Then the maximum rotational velocity may be calculated by Pythagoras: > > Max Rotational Velocity = ((M *1085)^2 - (V)^2)^0.5 > > where M is the designed Mach Number (0.85) and V is the > aircraft forward > velocity > > = ((0.85*1085)^2 -(440)^2)^0.5 = 810.52 > ft/sec > > RPM at Max rotational velocity is given by: > > RPM = Max rotational velocity*60/(PI * D) > > Where D is the propeller diameter (ft) > > = 810.52*60/(PI * 10.75) = 1439.98 rpm > > At 3000 rpm the propeller rpm is 1431 rpm, but the Merlin > only did this when > the throttle was through the gate, and the Boost Control > Valve Cutout was > operated. This was allowed for 5 minutes. > > We can calculate the Max Rotational Velocity @ 1431 rpm > > Max rotational velocity (PI * D) = (RPM/60) * (PI * D) > > = (1431/60) * > (PI * 10.75) > > = 805 ft/sec > > We can also calculate the Mach Number (M) of the tip by > rearranging and > substituting > > M = ((805^2+440^2)^0.5)/1085 > > = 0.8459 > > I hope that all the maths are correct. > > I think all this shows that under normal operating > conditions, and observing > the normal operating limit of 2850 rpm, it is unlikely that > the propeller > tips would exceed M1. > > Regards > > Vivian > Very clear, thanks, Richard ___ Flightgear-devel mailing list [EMAIL PROTECTED] http://mail.flightgear.org/mailman/listinfo/flightgear-devel
RE: [Flightgear-devel] Spitfire Propeller vs. YASim
Richard Bytheway wrote > Sent: 04 May 2004 10:42 > To: FlightGear developers discussions > Subject: RE: [Flightgear-devel] Spitfire Propeller vs. YASim > > > > I had already shown by some pretty simple math that at 2850 > > rmp the tips of > > a 1.65m radius propeller would be supersonic and therefore highly > > improbable, but we now know that the data of hp, gear ratio, > > rpm etc all tie > > together. > > > > Thanks > > > > Vivian Meazza > > > > I have a memory from years back of being told that the reason > the Spitfire had such a distinctive sound was that the > propellor tips _were_ supersonic. Maybe it was just heresay. > > Richard > I think it is possible that the propeller tips went supersonic in the corners of the flight envelope of some of the later versions. However, the math seems to show that in most circumstances they were not. It seems unlikely that this could explain the distinctive sound when heard from the ground. Here are some calculations on propeller rpm. The propeller the tip speed should be as high as possible with the only limitation being that the tip should not get into the region of aerodynamic compressibility. Typically a figure of Mach 0.85 is used as the magic number that should not be exceeded. (This makes some allowance for the speed increase as the air passes over the aerofoil curved surface and the increase in air velocity caused by the propeller operation.) If we take 8000 ft as the operating altitude then Mach 1 = 1085 ft/sec (approx) Assuming that the forward velocity of the aircraft is 300 mph = 440 ft/sec Then the maximum rotational velocity may be calculated by Pythagoras: Max Rotational Velocity = ((M *1085)^2 - (V)^2)^0.5 where M is the designed Mach Number (0.85) and V is the aircraft forward velocity = ((0.85*1085)^2 -(440)^2)^0.5 = 810.52 ft/sec RPM at Max rotational velocity is given by: RPM = Max rotational velocity*60/(PI * D) Where D is the propeller diameter (ft) = 810.52*60/(PI * 10.75) = 1439.98 rpm At 3000 rpm the propeller rpm is 1431 rpm, but the Merlin only did this when the throttle was through the gate, and the Boost Control Valve Cutout was operated. This was allowed for 5 minutes. We can calculate the Max Rotational Velocity @ 1431 rpm Max rotational velocity (PI * D) = (RPM/60) * (PI * D) = (1431/60) * (PI * 10.75) = 805 ft/sec We can also calculate the Mach Number (M) of the tip by rearranging and substituting M = ((805^2+440^2)^0.5)/1085 = 0.8459 I hope that all the maths are correct. I think all this shows that under normal operating conditions, and observing the normal operating limit of 2850 rpm, it is unlikely that the propeller tips would exceed M1. Regards Vivian ___ Flightgear-devel mailing list [EMAIL PROTECTED] http://mail.flightgear.org/mailman/listinfo/flightgear-devel
RE: [Flightgear-devel] Spitfire Propeller vs. YASim
Richard Bytheway said: > > I had already shown by some pretty simple math that at 2850 > > rmp the tips of > > a 1.65m radius propeller would be supersonic and therefore highly > > improbable, but we now know that the data of hp, gear ratio, > > rpm etc all tie > > together. At higher altitudes? IIRC when working on the p51d I figured just below 600mph was the speed of the propellor tips. The merlin had a slightly higher max rpm figure (3000) at that point. Best, Jim ___ Flightgear-devel mailing list [EMAIL PROTECTED] http://mail.flightgear.org/mailman/listinfo/flightgear-devel
Re: [Flightgear-devel] Spitfire Propeller vs. YASim
Richard Bytheway wrote: I have a memory from years back of being told that the reason the Spitfire had such a distinctive sound was that the propellor tips _were_ supersonic. Maybe it was just heresay. I don't know about the Spitfire, but I understand that's the case with many floatplanes -- you can usually tell when a plane flying overhead is a floatplane without looking up. All the best, David ___ Flightgear-devel mailing list [EMAIL PROTECTED] http://mail.flightgear.org/mailman/listinfo/flightgear-devel
Re: [Flightgear-devel] Spitfire Propeller vs. YASim
Richard Bytheway wrote: I have a memory from years back of being told that the reason the Spitfire had such a distinctive sound was that the propellor tips _were_ supersonic. Maybe it was just heresay. That probably was for the Harvard. Erik ___ Flightgear-devel mailing list [EMAIL PROTECTED] http://mail.flightgear.org/mailman/listinfo/flightgear-devel
RE: [Flightgear-devel] Spitfire Propeller vs. YASim
> I had already shown by some pretty simple math that at 2850 > rmp the tips of > a 1.65m radius propeller would be supersonic and therefore highly > improbable, but we now know that the data of hp, gear ratio, > rpm etc all tie > together. > > Thanks > > Vivian Meazza > I have a memory from years back of being told that the reason the Spitfire had such a distinctive sound was that the propellor tips _were_ supersonic. Maybe it was just heresay. RIchard ___ Flightgear-devel mailing list [EMAIL PROTECTED] http://mail.flightgear.org/mailman/listinfo/flightgear-devel
RE: [Flightgear-devel] Spitfire Propeller vs. YASim
Wolfram Kuss > > >Spitfire Mk IIA > > Ah - surprising! > > Here is an email Rick "Fuelcock" sent me a short while ago. I > hope it helps. Sorry for the poor formating. > --- snip - > Rather than send you the GBE code , I will direct you to the > site where I got > it: > > http://www.aeromech.usyd.edu.au/aero/propeller/prop1.html > > Just click on program 1 at the bottom of the page. Program 2 (right > below) > is mathlab code for the implementation without the bells and whistles. > > I have been playing around with program 1, and have obtained > very encouraging > results. > > I keyed in a "Spitfire" prop with radius 1.55 m and a blade > area of 0.98m^3. > The program only let's you design a simple blade with a > straight, symetrical > taper. Rather than complicate things, I just kept the cord > constant at .210 > the radius to give a total area of .327m^3 per blade. Not > knowing anything for > sure about the blade angle at a given radius, I just used the > default pitch > of 0.5, where: > > pitch = 2pi * r tan theta and theta is the geometric angle > of the blade at > r. The model also lets you tilt the whole blade +/- any > desired angle setting. > Assuming the max speed of the Spitfire to be 154.7 m/s, I > toyed with angle > setting until I obtained a max prop efficiency at angle > setting 19.45, J value > of 2.09, which corresponds to a true airspeed of 154.7 m/sec > for a 1.55 m > radius prop, engine running at 3000 rpm and gear ratio 0.477. > The model produced > a theoretical efficiency of about 85%, with Cq = 0.071. > > Next, I calculated the torque, using the formula Q=Cq * rho * > n^2 * D^4, > where n is prop rotation in revolutions per second ( the code > converts this to > radians) and D is prop diameter. > I assumed rho of 0.5 Kg/m^3, an altitude of about 15,000 feet. I than > multiplied the torque by angular velocity in radians per > second, to get the power > (watts) needed to counteract the torque of the prop. This > worked out to 865 KW, > which converts to 1159 HP. This is about 10% hiigher than what the > Merlin > could actually put out at the shaft, but it's pretty damn > good. Remember, the > model is known to be about 5% to 10% too optimistic in > predicting performance, > so if you take this into account, the prediction is nearly spot on! > --- snip - > > >Regards > > > >Vivian > > Bye bye, > Wolfram. > Why surprising? The choice was made with _impeccable_ logic: Eric Hoffman found the POH on the net, and I found some accurate 3d drawings in a book in my local bookshop. The math is helpful. At first glance some of the input data are a little off, but it shows the proposal, briefly made during the discussion on the performance of YASim, that 2850 was the propeller rpm, not the engine rpm at "cruise" cannot be sustained. I had already shown by some pretty simple math that at 2850 rmp the tips of a 1.65m radius propeller would be supersonic and therefore highly improbable, but we now know that the data of hp, gear ratio, rpm etc all tie together. Thanks Vivian Meazza ___ Flightgear-devel mailing list [EMAIL PROTECTED] http://mail.flightgear.org/mailman/listinfo/flightgear-devel
Re: [Flightgear-devel] Spitfire Propeller vs. YASim
>Spitfire Mk IIA Ah - surprising! Here is an email Rick "Fuelcock" sent me a short while ago. I hope it helps. Sorry for the poor formating. --- snip - Rather than send you the GBE code , I will direct you to the site where I got it: http://www.aeromech.usyd.edu.au/aero/propeller/prop1.html Just click on program 1 at the bottom of the page. Program 2 (right below) is mathlab code for the implementation without the bells and whistles. I have been playing around with program 1, and have obtained very encouraging results. I keyed in a "Spitfire" prop with radius 1.55 m and a blade area of 0.98m^3. The program only let's you design a simple blade with a straight, symetrical taper. Rather than complicate things, I just kept the cord constant at .210 the radius to give a total area of .327m^3 per blade. Not knowing anything for sure about the blade angle at a given radius, I just used the default pitch of 0.5, where: pitch = 2pi * r tan theta and theta is the geometric angle of the blade at r. The model also lets you tilt the whole blade +/- any desired angle setting. Assuming the max speed of the Spitfire to be 154.7 m/s, I toyed with angle setting until I obtained a max prop efficiency at angle setting 19.45, J value of 2.09, which corresponds to a true airspeed of 154.7 m/sec for a 1.55 m radius prop, engine running at 3000 rpm and gear ratio 0.477. The model produced a theoretical efficiency of about 85%, with Cq = 0.071. Next, I calculated the torque, using the formula Q=Cq * rho * n^2 * D^4, where n is prop rotation in revolutions per second ( the code converts this to radians) and D is prop diameter. I assumed rho of 0.5 Kg/m^3, an altitude of about 15,000 feet. I than multiplied the torque by angular velocity in radians per second, to get the power (watts) needed to counteract the torque of the prop. This worked out to 865 KW, which converts to 1159 HP. This is about 10% hiigher than what the Merlin could actually put out at the shaft, but it's pretty damn good. Remember, the model is known to be about 5% to 10% too optimistic in predicting performance, so if you take this into account, the prediction is nearly spot on! --- snip - >Regards > >Vivian Bye bye, Wolfram. ___ Flightgear-devel mailing list [EMAIL PROTECTED] http://mail.flightgear.org/mailman/listinfo/flightgear-devel
Re: [Flightgear-devel] Spitfire Propeller vs. YASim
Andy Ross said: > Vivian Meazza wrote: > > Here are some calculations on propeller rpm. > > [...] > > We can see that 2850 is unlikely to be the rpm of a 10.75 diameter > > propeller > > Yeah, you're right. This is a real bug. I was playing with it this > morning, and we're hitting an edge case in the propeller solver. > > The propeller as defined is actually fine. It sinks the right amount > of power and generates appropriate thrust at the specified cruise RPM. > The problem is that (due to a deficiency in the model) the torque > required to turn the propeller are *lower* RPMs increases faster than > the engine torque does*. So while the engine and propeller are > matched at cruise; the combination can't get there because it can't > accelerate the prop at low speeds. > > The end result is that this breaks the "stabilize" step in the solver, > which tries to iteratively solve for the steady state RPM for an > engine/prop before running the aero FDM. Mathematically, the current > propeller model has two minima, and it's picking the wrong one. > > The spitfire is hitting the condition because of the high gear ratio, > recent changes in the engine code which reduce available power at low > speeds (to get idle speeds right), and a miscalbration quirk in the > manual pitch handling (setting "0.5" for manual pitch doesn't produce > the same results as a non-variable propeller). > > I'm not quite sure what the right thing to do here is. One trick > would be to jigger the stabilize routine so it starts from an RPM > within the right range, but that's going to be really hard to > maintain over time. Let me think about it... > Any ideas on this yet? I caught a little bit of this thread before heading to NY and have been sitting on the edge of my seat ever since :-) It is an issue with the p51-d as well, of course. It'd really be nice to finally get that one right. Best, Jim ___ Flightgear-devel mailing list [EMAIL PROTECTED] http://mail.flightgear.org/mailman/listinfo/flightgear-devel
RE: [Flightgear-devel] Spitfire Propeller vs. YASim
Wolfram Kuss asked > I did not see the original thread. What Spitfire version are > you speaking about? > Spitfire Mk IIA Regards Vivian ___ Flightgear-devel mailing list [EMAIL PROTECTED] http://mail.flightgear.org/mailman/listinfo/flightgear-devel
Re: [Flightgear-devel] Spitfire Propeller vs. YASim
I did not see the original thread. What Spitfire version are you speaking about? Bye bye, Wolfram. ___ Flightgear-devel mailing list [EMAIL PROTECTED] http://mail.flightgear.org/mailman/listinfo/flightgear-devel
Re: [Flightgear-devel] Spitfire Propeller vs. YASim
Vivian Meazza wrote: > Here are some calculations on propeller rpm. > [...] > We can see that 2850 is unlikely to be the rpm of a 10.75 diameter > propeller Yeah, you're right. This is a real bug. I was playing with it this morning, and we're hitting an edge case in the propeller solver. The propeller as defined is actually fine. It sinks the right amount of power and generates appropriate thrust at the specified cruise RPM. The problem is that (due to a deficiency in the model) the torque required to turn the propeller are *lower* RPMs increases faster than the engine torque does*. So while the engine and propeller are matched at cruise; the combination can't get there because it can't accelerate the prop at low speeds. The end result is that this breaks the "stabilize" step in the solver, which tries to iteratively solve for the steady state RPM for an engine/prop before running the aero FDM. Mathematically, the current propeller model has two minima, and it's picking the wrong one. The spitfire is hitting the condition because of the high gear ratio, recent changes in the engine code which reduce available power at low speeds (to get idle speeds right), and a miscalbration quirk in the manual pitch handling (setting "0.5" for manual pitch doesn't produce the same results as a non-variable propeller). I'm not quite sure what the right thing to do here is. One trick would be to jigger the stabilize routine so it starts from an RPM within the right range, but that's going to be really hard to maintain over time. Let me think about it... Andy ___ Flightgear-devel mailing list [EMAIL PROTECTED] http://mail.flightgear.org/mailman/listinfo/flightgear-devel
RE: [Flightgear-devel] Spitfire Propeller vs. YASim
Vivian Meazza wrote > > Andy Ross > > > [Starting a new thread. The reply nesting level in my > > mozilla window was getting freaky.] > > > > Vivian Meazza wrote: > > > The engine I'm trying to specify developed 1140 HP at engine > > > revolutions of 2850 rpm at a boost pressure of 9 psi. It > was fitted > > > with 1:0.477 reduction gearing, which I think means that > > the propeller > > > turned at 1360 rpm. > > > > Hrm, 1360 RPM is very slow for a cruise value, just over idle > > speed for a smaller plane. Likewise, 2850 RPM really isn't > > that fast for a piston engine. It's at the top end of > > ungeared engines like a Lycoming O-360 or whatnot, but not > > really very fast for four stroke engines as a whole (my > > Saturn redlines at 6000, for example). > > > > Is it possible that the 2850 number is a *propeller* RPM at > > max power? Then you'd get a max power engine speed of 5975, > > which seems plausible to me and avoids the problems with > > solving for a propeller which "cruises" at a pitch where > > normal props would be windmilling. > > > > Does anyone have good info on whether the cockpit engine > > speed gauge in a Spitfire (which is presumably what most > > sources will quote for > > "RPM") reads engine or propeller speed? > > > > Andy > > > > > I believe the low propeller rpm was to do with tip speeds > approaching or exceeding Mach 1 at high aircraft speeds. I > will research that next. > > Regards > > Vivian > Here are some calculations on propeller rpm. The propeller the tip speed should be as high as possible with the only limitation being that the tip should not get into the region of aerodynamic compressibility. Typically a figure of Mach 0.85 is used as the magic number that should not be exceeded. (This makes some allowance for the speed increase as the air passes over the aerofoil curved surface and the increase in air velocity caused by the propeller operation.) If we take 8000 ft as the operating altitude then Mach 1 = 1085 ft/sec (approx) Assuming that the forward velocity of the aircraft is 300 mph = 440 ft/sec Then the maximum rotational velocity may be calculated by Pythagoras: Max Rotational Velocity = ((M *1085)^2 - (V)^2)^0.5 -(1) where M is the designed Mach Number (0.85) and V is the aircraft forward velocity = ((0.85*1085)^2 -(440)^2)^0.5 = 810.52 ft/sec RPM at Max rotational velocity is given by: RPM = Max rotational velocity*60/(PI * D) -(2) Where D is the propeller diameter (ft) = 810.52*60/(PI * 10.75) = 1420 rpm Thus we can see that 1360 rpm is more appropriate for this application than 2850 We can also calculate the Max Rotational Velocity @ 2850 Max rotational velocity (PI * D) = (RPM/60) * (PI * D) = (2850/60) * (PI * 10.75) = 1604 ft/sec We can also calculate the Mach Number of the tip by rearranging and substituting in (1) M = ((1604^2+440^2)^0.5)/1085 where M is the Mach Number of the tip = 1.5329 We can see that 2850 is unlikely to be the rpm of a 10.75 diameter propeller Well, I hope I've got the math right! Please pick holes in it. Regards Vivian ___ Flightgear-devel mailing list [EMAIL PROTECTED] http://mail.flightgear.org/mailman/listinfo/flightgear-devel
RE: [Flightgear-devel] Spitfire Propeller vs. YASim
Andy Ross > [Starting a new thread. The reply nesting level in my > mozilla window was getting freaky.] > > Vivian Meazza wrote: > > The engine I'm trying to specify developed 1140 HP at engine > > revolutions of 2850 rpm at a boost pressure of 9 psi. It was fitted > > with 1:0.477 reduction gearing, which I think means that > the propeller > > turned at 1360 rpm. > > Hrm, 1360 RPM is very slow for a cruise value, just over idle > speed for a smaller plane. Likewise, 2850 RPM really isn't > that fast for a piston engine. It's at the top end of > ungeared engines like a Lycoming O-360 or whatnot, but not > really very fast for four stroke engines as a whole (my > Saturn redlines at 6000, for example). > > Is it possible that the 2850 number is a *propeller* RPM at > max power? Then you'd get a max power engine speed of 5975, > which seems plausible to me and avoids the problems with > solving for a propeller which "cruises" at a pitch where > normal props would be windmilling. > > Does anyone have good info on whether the cockpit engine > speed gauge in a Spitfire (which is presumably what most > sources will quote for > "RPM") reads engine or propeller speed? > > Andy > I pondered that question for quite a while before I decided to use that data. And I agree that the max engine rpm sounds low when compared to modern engines, particularly modern automotive engines. Propeller rpm seems impossibly low, and I wondered if I am misinterpreted the meaning of the published gear ratio of 1:0.477. All documents that I have seen quote the max engine of the Merlin as 3000 (2850 is the max cruise). Similarly, all the POH (Hurricane/Spitfire/p51d) quote the cockpit instrument as "engine rpm" Compare the 2 engines Bore 5.4 in, Stroke 6 in, Displacement 1,649 cu in (27 litres). Max rpm 3000 Bore 3.38 in, Stroke 3.46 in, Displacement 180.75 cu in (2.962 litres) max rpm 6000 This is a rough formula derived for automotive applications. A piston speed of 3500 fpm is usually quoted as an estimate for non-high performance modern engines. RPM limit = (Piston speed (fpm) * 6) / stroke (in) If we take the Saturn data, and re-arranging, we get: Piston Speed = 6000*3.4/6 = 3460 fps We can see that the Saturn complies with this paradigm. Now taking the Merlin data: RPM Limit = 3500 * 6/6 = 3500 rpm We can say that it is highly unlikely that the Merlin engine would have been capable of achieving the 6290 rpm required if the max rpm were quoted as propeller rpm. This would call for a piston speed of: Piston Speed = 6290 * 6/6 = 6290 fps 4000 is usually quoted as the maximum for high performance engines, although the modern F1 engine exceeds this, 4000 would be a reasonable limit for a 1930's engine I think it is safe to assume that the rpm quoted for the engine rpm for the Merlin is indeed the engine rpm. I believe the low propeller rpm was to do with tip speeds approaching or exceeding Mach 1 at high aircraft speeds. I will research that next. Regards Vivian ___ Flightgear-devel mailing list [EMAIL PROTECTED] http://mail.flightgear.org/mailman/listinfo/flightgear-devel
