Hyperion
Emeter
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HYPERION Emeter |
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Hyperion Prop Talk Objectives In this section of the Hyperion Website, the intention is to introduce the concept of prop constants along with values for a number of popular propellers. There are a number of different ‘constants’ in use in the model aircraft scene; here we talk about those which can be used to relate motor output power to the prop rpm achieved. We specifically will not be covering thrust constants which can be used to estimate the static thrust of a propeller at given rpm. Nor will we cover motor ‘constants’ such as the rpm per volt, idle current and winding resistance, important ‘though these are for determining motor performance characteristics It does not pretend to be an exhaustive coverage of the subject, but is a background into the use of ‘constants’ for propeller evaluation, especially with the Hyperion Emeter. So, we will include various definitions, formulae, rules and a method of measurement. We then describe a few ways in which you can use the information included in this Web Site to your advantage. Introduction Most electric flyers want more performance, in the form of speed, climb rate, duration, aerobatic ability or miniaturisation. These days with efficient, light brushless motors - such as the Hyperion ‘Z’ and ‘X’ series - we can enjoy performance levels undreamt of 15 years ago and, yet, we still want more. One of the simplest ways to alter performance for the better is to identify the ideal propeller for your model. The driving force behind (or in front of) most electric planes is the propeller. Props come in many varieties with different diameters, pitches, blade counts and shapes. Unlike internal combustion engine power, electric motors can turn a large range of sizes, sometimes well and sometimes so badly that eventual damage to the powerplant will result. It is good to know beforehand just what load any given propeller is going to place on the motor. The load on the electric powerplant is very largely a function of the prop size, however more load and size does not always equate to more performance, even though more power will be drawn from the flight pack. In fact, the best performances of an electric powered model always require that the propeller be matched to the motor, gearbox, Electronic Speed Control unit (ESC), flight pack and to the type of aircraft. This might, at first, appear to be a daunting task but, by breaking it down into small steps, success can be achieved Diameter and Pitch The diameter of the prop is nominally a very simple measure which is still commonly expressed in inches, despite metrication. However, a little complication is introduced with folding props which are fitted with varying sizes of centre-piece. These may vary from 30 mm to over 50 mm pivot bolt centre distances, so the total prop diameter could vary by nearly one inch. This would have a major effect on the load on the motor as will be seen below. The pitch of a propeller is a little less clear. Many liken it to the forward distance moved if the prop were being screwed one revolution into a solid object. Pitch is a measure of angle of the blades at a given distance from the centre - with a zero degree angle (ie one cut from a flat disc), the prop would give no forward motion, whilst a 90 degree angle would also give no forward motion, but a large sideways draft. Somewhere in between is a useful range of angles! However, the angle of the blade is not constant. Near the tip, the angle will be relatively low compared with the angle closer to the centre. If this were not the case, the fast moving tip would be try to accelerate the air much more than would occur at the centre. The efficiency of the propeller would be very low due to the difference in slipstream speeds when moving from the tip to the centre. To make matters a little more complex, manufacturers often do not aim for a constant pitch from centre to tip, again in the interests of efficiency. Thus the tip may well have less pitch than at nearer the centre. In this case, how can a simple number of inches describe the pitch? Aeronaut charts the pitch of their large range of propellers with figures given at the 75% diameter point to overcome this problem. A useful measure to describe a prop is the ratio of diameter to pitch which usually falls in the range of 4:1 down to about 1:1 Another analogy to explain the significance of pitch is to liken it to the gear ratio in a car. If a low gear is chosen, then the initial acceleration and ability to climb steep hills would both be good, but top speed would be limited by the engine rpm limit. If top gear is chosen, then hill climbs and initial acceleration will suffer, but the top speed is potentially much higher. In the same way, a low pitch propeller allows for steep climbs but at a low speed, whilst higher pitches are used for faster speeds in racing models, particularly with level flight. As a rough guide, start with the following diameter to pitch ratios for the listed differing applications:
Some General Rules for Propellers Here we will concentrate on the questions of:
There are a number of established rules which apply to the use of propellers:
Taking these three points, the power in watts required to drive a prop would be: Watts = Const * rpm3.0 * diameter 4 * pitch This formula, however, suggests that the diameter, pitch and rpm are the only three factors determining the power, which is far from the real-life case. Some performance prediction models therefore use a different constant for each family of props, such as 'Aeronaut Cam Folder' or 'APC fixed'. In fact, though, even this is too much of a generalisation since it depends on the accuracy of the manufacturers figures, and assumes all propellers in a series are identical in design - which is not the case. By way of example of this accuracy problem, one now-obsolescent 14 * 8.5” folder had an actual measured pitch of about 6"! And we have found many other examples of propellers in our testing which either overstated or understated the true pitch and even diameter. Some further examples of anomalies are given in the individual discussions, later, on each family of prop. The solution we have chosen is to establish two prop constants for each and every prop individually. The first of these is, traditionally, given the value of 3.0 as shown in the above formula, but we find variations to this precise cube law. With literally hundreds of different props on the market and near endless variety on offer for folding props by means of different sized and angled centre-pieces, the task of cataloguing them becomes enormous. However, nothing ventured, nothing gained, as the saying goes! We welcome any constructive comment and additions to our data and understanding on the subject. We have explained the sources of published prop constants to assist in this refinement process. Measurement of Prop Constants First, we need to explain the relationship between torque, rpm and power. At steady rpm the torque or ‘twisting strength’ of the motor will exactly match the drag or resistance to turning of the propeller, (otherwise the rpm would increase or decrease). Torque is measured as a force at a certain radial distance eg ounces*inches, grams*centimetres or Newtons*meters. In fact, the formula can be shown to be: Watts = RPM * Gms-Cm / 97400 Measurement of torque is normally carried out with a dynamometer. We use just such a unit for our testing. A motor and controller are mounted in a tube which is supported by two low-friction ball races. With a prop on the motor output shaft, the tube will attempt to rotate in the reverse of the prop direction and, via a simple lever system, presses on a set of accurate digital scales. The length of the lever is adjusted to a give a radius of 4.87 cm, so, applying the above formula, the power required to drive the prop at any given rpm is RPM * gms / 20000 There are a number of potential inaccuracies, most of which have been addressed, with torque, power and efficiency measurements, including:
From the earlier equation of Watts = Const * rpm ^ 3, the dyno gives us the rpm and the watts, so we can calculate the constant. In fact, by running the motor at several different throttle settings, we can not only improve the accuracy of the constant, but can also confirm or revise the cube law rule. (See comments on Aeronaut folders and the cube law below) Motor Efficiency Calculations and the Operating Point Once you have established the power in Watts required to achieve the measured prop speed, it is then a simple matter to calculate the efficiency of the ESC, the motor and the gearbox. Just divide the output power by the input voltage and current and multiply by 100! The Hyperion Emeter does this for you in real-time. Start by entering the Prop Constant and Power Factor from the accompanying tables for the prop which you are using. Connect the Emeter shunt into circuit as per instructions and hold the tacho up to the prop. Switch the motor on, wait for the readings to steady and the efficiency will be displayed. Press the hold button on the Emeter so that you can study the results at your leisure. Of course, you could also do this with an ammeter, a voltmeter, a tacho, pencil and paper and a calculator – as long as you can record three figures simultaneously and correctly!! For any given motor, gearbox, ESC and battery pack combination; there will be two operating points of primary interest. These are the maximum efficiency and the maximum power points. You can move to either point or anywhere in between simply by changing the propeller. Installing a too-large propeller moves you past the maximum power point, and turns most of the power in the system into heat which damages your motor and/or battery. Note that for high power applications with modern, low-resistance motors, the maximum power point is often determined by the current capacity of the flight pack cells, whereas the maximum efficiency is determined largely by the motor and ESC. Let’s use an example in which the maximum efficiency is at 20 amps current draw and the maximum power is at 40 amps. Fitting a prop which draws less than 20 amps would result in a sub-optimal performance; a change to a larger prop would enjoy the double benefits of increased powerplant and propeller efficiencies. Likewise, choosing a prop which draws 50 amps would not only result in a reduction in power level, but could well cause damage to the battery, motor, or ESC. In this example, you would want to operate close to the 20 amp point for the longest motor run times and close to the 40 amp point for the most short time power, such as Limited Motor Run glider competition. By carrying out tests with different props, the Emeter, with prop constants entered, in tacho mode can tell you whether you are exceeding maximum power and, in motor mode whether you are operating efficiently. Note that this efficiency figure is for the combination of ESC and motor and the gearbox and may well be less than that quoted by the manufacturer for the motor alone. Either manual or Emeter techniques will require that you know the prop constants so let’s move on to the details Aeronaut Folding Props We start the detailed discussion with this renowned German manufacturer of both folding and fixed bladed props, since they have offered the general modelling public a wealth of invaluable data about their products. Aeronaut, on the following website pages effectively specify individual prop constants by plotting power against rpm for the Classic and Cam folder series. http://www.aero-naut.de/prop/bilder/gross/diagrammCAM.jpg http://www.aero-naut.de/prop/bilder/gross/diagrammCLASSIC.jpg Elsewhere, they also tabulate the rpm for 100 watts of power driving the propeller with a number of different sized centre-pieces and with five different angles from minus 5 degree to plus 5 degrees. This rpm figure is often called the N100 figure It is interesting to note that the graph and table figures do not always agree. For example, the 18*11 Cam folder is shown as 3150 rpm for 100 watts input from the graph, but 3070 rpm from the table. Since it is not easy to read exact figures from a graph, our preference is to use the table figures. However the graphs do show one important point: they suggest that the relationship between power and rpm is not an exact cube law. A careful examination at both ends of the graphs rpm/power scale shows that, for Aeronaut folders, a better fit between graph and formulae is to use a power factor of 3.08 rather than the generally accepted figure of 3.0. So, the general formula of: Watts = Prop Const * rpm ^ Power factor Becomes: Watts = Prop Const * rpm ^ 3.08 for Aeronaut folding props. If we measure rpm in thousands, then this gives a handy value for the prop constant eg 0.1 to 4.5. There are other variables which will give inaccuracies of a lesser magnitude, such as temperature, humidity and altitude which we will not attempt to cover here, but one item is important: Centre piece size must be considered; a change from a 42 mm to a 47 mm centre piece on a 14" folding prop would give about a 1.7% increase in diameter. This amounts to a significant extra 7% in power being needed for the same rpm (due to the power-of-4 relationship). In the accompanying page, we have derived Aeronaut constants for the 52mm, 47mm and 42mm centrepieces and assuming a power factor of 3.08 in the formulae. Independent tests have been conducted with the electric motor dynamometer and these have shown general agreement with the Aeronaut Website figures. Two notable exceptions are the 14*10 and 15*10 Cam folders. In every test carried out with one sample of each of these sizes, the 14*10 prop has been found to load the motor more heavily than its larger counterpart. Much of this anomaly can be explained by the differences in pitch with the smaller prop having an 11.2” quoted pitch compared with 9.8” for the larger 15” version, according to Aeronaut themselves. In these tests, carried out over a range of rpm, virtually every prop showed a better match to the formula by using a power factor of 3.08 rather than 3.0, confirming the analysis of the Aeronaut graphs In other tests, a brushless Hectoplett pylon motor with added gearbox and a 12.5*7.5 Cam /42 mm prop was found to record 8.54 volts, 53.1 amps and 7605 rpm. From the Aeronaut constants page, we see an AN figure of 0.623 which gives an efficiency of only 71%, whereas the dyno measured constant of 0.691 yields 79%. Knowing the quality of this motor, the dyno based results seem more realistic in this case at least. We also show data in our charts on Aeronaut folders which was compiled by Mr. Wilhelm Geck from Germany. In his results, he quotes the output power and rpm, from which prop constants can also be calculated. There is evidence within these figures of an adjustment to make them fit the cube law rule; however we have tabulated these results assuming a power factor of 3.08. So, for Aeronaut folding props we have, in some cases, three different values from which you can choose, all of which are fairly close in agreement. An average figure is shown, which might be the best alternative for the moment. APC Electric “E” Props Most of the props in this extensive range were tested on the dynamometer to establish the torque required for a given rpm. Whilst this equipment is not the most expensive available, results do agree with expectations from other spot checks. Each prop was subject to between 5 and 10 such tests at different power levels. Virtually all those tested showed a much better fit (ie a more constant ‘prop constant) by using a power factor of 3.2, instead of 3.0. The ‘square’ or near-square props (ie those with an equal pitch and diameter figure) appear to be the exception and, for these, a power factor of 2.9 gave the best fit. The difference may be attributed to the fact that the high pitch props are stalled during bench tests and, therefore, operate to a different rule at static testing. For purposes of establishing motor system efficiency, this is irrelevant, but do keep in mind that static current levels for highly-pitched props may change significantly (rise) in flight. APC Sport Props This range of props is also very extensive and has been tested with Mega motors by Wilhelm Geck. In the absence of any other published information on the APC Sport series, we have simply calculated the propeller parameters. Any sizes which have been tested on the dyno are shown in the table. A power factor of 3.0 has been assumed, in the absence of any other evidence Aeronaut Fixed Electric Props Data for this series of props has been taken directly from the Aeronaut Web Site. A power factor of 3.0 has been assumed, in the absence of any other evidence Graupner Carbon folders Figures for this series have been taken, largely from the test results of Mr. Geck, applying a power Factor of 3.08, in line with the findings on Aeronaut folders. The 14*9.5 prop has been tested on the dyno and was found to yield a more accurate constant with a power factor of 3.08 than 3.00 Graupner Speed CAM props. These have been tested by various means on many occasions including the use of two different dynos. The results in the table have been refined over several years. A power Factor of 3.0 has been used. Some ways to use the prop constant and efficiency figures
Suppose you want to increase the power of your model.
Assuming that you have checked the current draw (with an Emeter, of course)
and found it to be well below the rating for the flight pack, ESC and the
motor, then you have the choice of using a larger prop. If you find it necessary with a geared motor to fit a very small prop in order to reach a high efficiency, then it would be worth considering a higher gear ratio and fitting a larger diameter prop with appropriate pitch to maintain target air speed. Remember that the prop efficiency itself decreases as its size falls and may well counter the gain in motor efficiency. At reduced throttle settings, you should be aware that some brushless ESCs display a much reduced efficiency at part throttle settings. Now, inefficiencies in any electrical component usually shows itself as extra heat, so take care to avoid prolonged partial throttle runs with a low efficiency controller/motor. How do you tell if your ESC is displaying this problem? Just couple up the Emeter, enter the two prop constants and test it for yourself over a range of throttle settings! By the way, you must wait for the steady reading to occur after reducing the throttle – you will notice a false short-term increase in efficiency as you throttle back because the inertia of the prop maintains higher rpm and the current drops to below its steady reduced value. Finally, please note that differences in temperature, humidity, barometric pressure, and altitude can all affect the efficiency figures you record. Differences in ESC type, resistance, and the settings in the ESC for timing advance and frequency can also affect readings. So remember that the data you collect is primarily useful, and completely accurate, when used to compare motors and propellers on you own equipment at your own location. To make absolute statements about efficiency for a particular motor brand or type would require an extremely well-controlled laboratory environment. So please refrain from over-generalizing your results in discussion, as a fine motor could be unfairly maligned due to inappropriate comparisons. Have fun and we hope you have found useful this introduction to props, power constants, and power factors - and how they allow us to easily determine the efficiency of a power system using the Hyperion Emeter. Best Regards,
The Hyperion Team If you found this page via a search engine, you may like to take a look at the Hyperion Emeter datasheet by clicking here.
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