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Old 03-15-2009, 12:01 PM   #76
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John - I attach two gifs from my first pass at the Hacker 13.5 in CircuitMaker Student Version of SPICE. Input data taken from the spreadsheet Matt put up:

Quote:
The Sentry Dyno Calc spreadsheet is almost completed. Here you go guys, big preview. Be sure to give John a lot of kudos for this, he is a mathematical genius!

http://arcadechamp.net/radio/Hacker,...2%20x%202.html
I was about to list my input matrix, but found a small error, so I'll run again and repost that result. I'm used k = 0.00345 but it may be k = 0.00348.

The thing I note here is my graph gets to peak power Pmpk right about the same time as your sample data, tpk = 1.4{s}. My magic formula for air gap power predicts:

Pmpk = (1/4)*[Vs^2/(Rs + Ra)] = 0.25*[8.4^2/(0.006 + 0.073)] = 222{W}

When you add the bearing dissipation to the peak flywheel power you get back the air gap power predicted by the "magic formula." This is listed in some references and you can derive it yourself from Kirchoff's Voltage Law in the motor circuit and Newton's Second Law in the mechanical differential equation. I am not sure why your power is coming up 215 Watts on the flywheel or where the error might be at this point, which is what I meant by "triangulation."



Note: I'm calculating Ra and k as if this were a brush motor, and it may be there is a correction factor that must be applied, because in the brushless motor there are always two phases of the coils active at an instant of time. I still doubt that a change in flywheel inertia should alter peak power output in any case, just as adding or removing mass (inertial load) from a rolling chassis does not change the peak horsepower output from the installed engine.
Attached Thumbnails
Novak Sentry as Brushless Dyno-hacker_13_5_0deg_ckt.gif   Novak Sentry as Brushless Dyno-hacker_13_5_0deg.gif  

Last edited by SystemTheory; 03-15-2009 at 01:06 PM.
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Old 03-15-2009, 02:18 PM   #77
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John and Matt,

The Electric Flight clan usually says good things about motocalc, although I didn't find the program very enlightening during the free trial period, since I can get much better waveforms in a free version of an engineering simulator. I think it is limited to using a gearbox and propellor, which give a unique load feedback to in flight system.

However there is a very good discussion of measuring motor parameters, for brush motors and brushless motors, in the published User's Manual, on the bottom of page 20 through page 23 of the PDF document found here:

www. motocalc.com/viewman.htm

I regard the measurement of k using a drill, rpm sensor, and voltmeter as highly reliable, since the motor operates in generator mode with no electrical load, so k = V/omega computes clean. To do this with a brushless motor, you must build an inexpensive 3 phase rectifier circuit, as described in the manual, and this also appears to give a reliable measurment of k (at the magnet temperature when taken).

The measurement of armature resistances is also reasonable, although it does not discuss instrument sensitivity or temperature dependencies, and I insert this quote for how it is done for a brushless motor:

Quote:
Measuring the Armature Resistance (of a Brushless Motor)
Connect two terminals of the motor to a variable voltage power supply, with an ammeter in series with one of the leads, and a voltmeter across the two motor terminals. Leave the third motor terminal unconnected. Keep the motor shaft from turning by holding it with pliers or clamping it in a vice. Slowly increase the voltage until the current reaches 5A or so (or half the rated safe operating current of the motor, whichever is less). Divide the measured
voltage by the measured current, and then multiply that by 0.875 to get the armature resistance.
Unfortunately if I take my estimate of Ra = 7.74{V}/106{A} = 0.073 taken at the first sample point in Matt's spreadsheet, then multiply by the factor 0.875as described above, then plug adjusted Ra into my model or magic formula, I get Pmpk = 234.4 Watts in the flywheel, an even greater error.

Anyway I hope this extra information is helpful although perhaps a bit frustrating while you sort out the Dyno results.
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Old 03-15-2009, 02:20 PM   #78
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Our motor torque is the result of a measure. T= I x angular acceleration.

We measure I, We measure angular velocity and derive angular acceleration to get power. The physics is very straight forward. Since Inertia (I) is used to calculate power then of course changes in I must be accounted for in calculating motor power. Certainly if you cut the flywheel inertia in half, the motors max power can be the same, but to measure this power using our method you have to cut the inertia in half in your calculation. This is not a difficult concept. Flywheel dynos like the dynojet full size car dynos use these methods to measure power routinely. You have to know the Inertia of the roller (or flywheel) when you take our very common approach at calculating power.

Checking our number would be as simple as dynoing the motor under similar conditions on a second dyno with a different RPM sensors. It is in my opinion unlikely to think that our number is the one in error since it is measured directly. Whereas yours is measured obtusely but with data from a real dyno. Now if the precision or repeatability of our dyno is not there it lessens somewhat the usefullness but it is still useful. My main use is the RPM at peak power. That should be a very good result.
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Old 03-15-2009, 04:25 PM   #79
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John,

If you trust the rpm sensor most of all, I find that reasonable, and maybe I'll adjust my parameter estimates off of that, just to see if I could build a good predictive model of system behavior. Of course you have such models in mind already for racing purposes and my interest is to gain greater insight into the system design and perhaps develop a robotics and technology education module to publish interesting case studies in a virtual classroom.

In terms of checking your peak power versus rpm point, you might also use the same Dyno with a different flywheel inertia, perhaps one of the same dimensions but a different density of material. If my hunch is right, you will get a similar peak power number, it will come sooner or later in time, and at the same rpm, other factors kept equal.

Is there anything in your calculations that contradicts that possibility? That is what will occur in my model if I adjust it to make peak power exactly in accord with your measurements, then simply change inertia up or down holding other parameters constant. I find this significant since it helps me anticipate the time response when a gearbox and chassis are attached to the motor and tires are coupled to a surface via full traction.

On the earlier thread of gear ratio selection, you said the other guys were up by 5-6 teeth (on the pinion?), and motors hot like a frying pan. I assume the hot like a frying pan motors had a lower overall ratio G? Is this correct? I am still considering why you ran cooler and they ran hotter at comparable lap times, and why your gear selection did not give a better advantage.
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Old 03-15-2009, 07:31 PM   #80
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"In terms of checking your peak power versus rpm point, you might also use the same Dyno with a different flywheel inertia, perhaps one of the same dimensions but a different density of material. If my hunch is right, you will get a similar peak power number, it will come sooner or later in time, and at the same rpm, other factors kept equal. "

System Theory

I agree with this. I posted the equivalent in my previous post.
when you use this light flywheel, however, you have to input the new flywheel inertia into the calculations of a flywheel dyno and add the motor rotor inertia for best accuracy.

You have quoted my oval experience accurately. Yes the other guys ran with a lower numerical overall ratio, or higher rollout. There are many factors that affect lap times on the oval. Only one of them is motor power. Equally important on flat oval is having an optimum line. Scrubbing less speed in the corners. Oval guys are able to drive this optimum line better than road racers. I think they were gaining .1s with a better line and then losing .1s with a poor gear ratio. I tried the big pinions. The car just became numb. It would not accelerate but would not decelerate much either. Pan cars are a bit ticklish coming out of a corner. They may have relied on this to provide stability on corner exit. Tire choice is equal in importance to motor power and proper line. Last comes setup at maybe 5% assuming the car is not ill handling.

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Old 03-15-2009, 08:27 PM   #81
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John, you must be aware of the gearbox as an inertia transformer. You say when G goes down the rollout goes up. The way I see it, the time and distance to maximum speed goes up too because it takes more time to spin up a bigger equivalent flywheel inertia, the back-emf voltage goes up slower, causing the high current draw to last longer, so too much gear overworks the motor, heating it up like a frying pan.

The flywheel inertia "seen by" the motor JLm (load reflected to the motor) includes the mass m coupled through traction at tire radius r, plus the equivalent inertia Je in the driveline, so I figure it may be one of two possibilities, or somewhere in between (with some data I might nail this down):

1. JLm = (mr^2 + Je)/G^2; or
2. JLm = (0.5mr^2 + Je)/G^2

and you can plot these values as a curve by creating an array of acceptable gear ratios G_low ... G_high in a spreadsheet to gain some insight.

Now when I first looked at this, I figured reducing G will heat up the motor with higher current, but since you make more torque, you'll go faster all the time. But then I speculated (no data here) that the drag force and driveline damping get reflected back in proportion to G^2, and this probably explains why your buddies were running so darn hot. On the power curve you draw a lot of current to pull a bigger flywheel JLm, and you draw extra current to fight a higher reflected damping, if my theory is correct. So you can get pretty hot with no systemic advantage (driver feel is something you are the expert in, not me). It seems to me the Novak Dyno could be used to gather some data if sensored properly, also a gearbox could be used with more powerful motors to limit the top flywheel speed, once one understands the basic testing methods, possibilities open up.

I wrote some code in Numerit Pro to check your P = I(dw/dt)w methodology and visualize it for myself. I get back a pretty good fit with one exception, the total time must be set to tF = 9.7{s} to hit the peak power, maximum acceleration, maximum torque, and time to peak power almost on the button! I only assume an exponential angular velocity curve defined via a standard equation:

w = wmax*(1 - e^(-t/tau))

take the numerical derivative to get acceleration, multiply by I to get torque, then P = T*w to get power, and pick off the maximum power points.

The only challenge this demonstrates is the choice of cut-off time on the dyno, where if I set my time array 0 .. 7 seconds instead of 0 .. 9.7 seconds the peak power shoots way up. I don't know if this assists you with thinking about a consistent time cut-off process in the data, since the exponential model would require a move to within 98% of the infinite speed, which in math is never reached. Am I missing something or onto something in terms of getting consistent pulls?

Last edited by SystemTheory; 03-16-2009 at 09:12 AM. Reason: improve clarity
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Old 03-15-2009, 08:49 PM   #82
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Below is what Numerit code looks like. You can write up to 60 lines in the free evaluation version on a Windows XP or Vista OS, in a code editor, then set up graphs and equations, whatever, in a Report panel, so this is a nifty tool.

Numerit.com offers the free edition of Numerit Pro.

This is my code with comments:

`Discrete Time Resolution and Spin Up Time Adjustment
n = 101 `# data points in each array
tF = 9.7 `{s} projected spin up time

`Hacker 13.5 on Sentry Dyno
wmax = 2205 `{rad/s} maximum angular speed
Jm = 4.138E-07 `{kg-m^2} rotor moment of inertia
JL = 3.45E-04 `{kg-m^2} flywheel moment of inertia

`Time Array and Time Constant
t = 0 .. tF len n `{s} spin up time array
tau = 0.2*tF `{s} system time constant

`Angular Velocity Array
w = wmax*(1 - e^(-t/tau)) `{rad/s} angular velocity as exponential curve
wP = wmax/2 `{rad/s} peak power velocity
tpk = interp(t, w, wP) `{s} time of peak power point

`Angular Acceleration Array
a = aderiv(w, t) `{rad/s/s} derivative of velocity
amax = max(a) `{rad/s/s} maximum angular acceleration

`Flywheel Inertia
J = Jm+JL `{kg-m^2} moment of inertia

`Torque Array
T = J*a `{N-m} torque into flywheel
Tmax = max(T) `{N-m} maximum torque
TP = Tmax/2 `{N-m} peak power torque

`Power Array
P = T*w `{W} power into flywheel
Pmpk = max(P) `{W} peak flywheel power

I get these data points marked on graphs and printed to fields in my Report:

2205 {rad/s} maximum angular velocity
1120 {rad/s/s} maximum angular acceleration
0.3869{N-m} maximum torque
216{W} peak power at time = 1.34{s}

These are very close to the ones published for the Hacker 13.5 except for total time.

Any small adjustment of time changes the power a little, and if I change the resolution n of data points in the array, it changes the data points a bit too, but not too much.

The file type can't be attached unless I zip it, I think. If anyone wants it I'll try to post it up.
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Old 03-15-2009, 10:13 PM   #83
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Here is the finished Novak Sentry Dynocalc Spreadsheet in excel. I have put instructions on sheet 3 of the excel spreadhsheet. It includes one set of data.

I have included a box to enter the inertia of the motor armature. This is added to the flywheels inertia automatically. Here are the instructions to use the spreadsheet to obtain dyno data from the Sentry dyno that Matt built. Maybe later we can have some pics.

Start your data entry at the first uptic in amps or RPM. Include one previous point. The spreadhsheet will assume the previous point is 0s and the next point .1s and so on. You don't have to manipulate the time data column.

How to use spreadsheet:
1 Use the File Save as command to make a duplicate of the spreadsheet. Include the motor name and the date in the title of the new file. Close this file and then reopen the new file
2) Copy and paste data from Sentry into the Data Input Boxes marked in green
3) Format RPM column to show 0 dec places
4) Enter flywheel moment of inertia and motor armature moment of inertia in the box at the far right marked in green
5) Enter in Motor type and notes at the far right in the box marked in green
6) Delete Unused rows from Sheet 1 and Sheet 2
7) Print sheet two page 1 for a nice output graph, Print sheet two page two and three for a list of all the calculated outputs.

This spreadsheet should work fine with Fantom and Robitronic Data. The first file is excel the second file is open office. The Dowload is Still not working file is corrupted. I'll see if Matt can post it.

I can e-mail copies send a request to [email protected]

System Theory-Does that mean we are in agreement on output now.

Last edited by John Stranahan; 03-16-2009 at 04:02 PM.
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Old 03-16-2009, 09:03 AM   #84
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John, I lost another good post! I agree with the power calculation in the flywheel + motor based off the rpm sensor with a curve fit to the data. The accuracy is of course a calibration question which you've left to Novak, but the measurement techique I agree with and appreciate your patience while I thought it through. There's a 100A limit on the current sensor which may throw off efficiency numbers in the turn-on region for more powerful motors. If one can trigger data capture off either the current or rpm sensor it seems to me the current sense (although maybe not accurate over 100A) is the best bet since the speed sensor lists a lower limit of 500 rpm.

I'll continue to work on my models since it should be possible to fit your data to the standard solution for the differential equation, within reasonable error. I'm impressed with the work you and Matt have put in on the project.
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Old 03-17-2009, 11:38 AM   #85
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I have the spreadsheet with Hacker 13.5 data, thanks John and Matt.

I attach a sketch of load line analysis to help me interpret the Dyno data. For those who are not engineers, a load line analysis is the graphical solution to an input-output system where you plot the source characteristic against the load characteristics to find an equilibrium point and study dynamic transitions.

This approach assumes the brushless motor is operating much like a brush motor through the electronic speed control, which appears to be reasonable based on the data you're getting off the Novak Sentry Dyno. I am still testing this hypothesis which is the point of studying the details further.

I'm applying a Simplified Linear Model for an Armature Controlled DC Servomotor, described in my old textbook, Control Systems by Naresh K. Sinha, in section 2.4 on page 13. This model has a differential equation as I posted above, with one change of notation, let bearing damping br -> D, and the Greek letters are used for symbols which we can't do here. Nonlinear models are available to explain why measurements might deviate from this model, but that is way too complex to get into here, and probably not necessary.

In this graph, time begins at t = 0 on the left axis when open circuit source voltage Vs is first applied to start the Dyno test. The air gap converts electrical power input to a mechanical power source at the air gap line. This source of mechanical power (Watts) goes into two mechanical sinks, to increase the kinetic energy of the inertial load of the rotor + flywheel as it spins faster, and to overcome the increasing counter-torque due to friction in the bearings (and brushes for the PMDC).

The operating points in the source and the two loads are coupled and move to the right over time, where time increases with more inertia Jeq in the motor and flywheel, if all other factors are kept constant (a difficult thing to do in an actual Dyno, which is where design optimization comes into play).

The Novak Sentry appears to do a good job of detecting speed/rpm at the flywheel, and John's data smoothing with calculations produces the BLUE line. In Dyno tuning for Racing, you'll want to minimize the damping loss in the bearings and/or brushes (RED line), since this saps power away from acceleration. In a brush motor this is the purpose of having a Dyno to select springs, brushes, and correct for commutator wear, etc., you can better optimize the motor. Assuming the air gap source is at a constant slope, less power at the RED line means more power into the flywheel on the BLUE line.

However out on the track one encounters heating effects and battery discharge curves, which tend to decrease the slope of the line for the air gap source. These effects can be made worse by poor gear selection for a given track. Thus to interpret the Dyno results for given motor I agree 100% with John, and respect his experience, the Dyno is a great tool. But to understand power fade, fuel economy in electric vehicles, and gear selection, one must track back the changes in slope of the air gap line to the electrical parameters in the battery curve and motor, which I call "the motor circuit parameters." These pass through the air gap due to the Conservation of Power and appear at the end-points (and impact the slope) of the air gap line.

Anyway I wanted to post up this diagram for criticism or comment since I am getting very good simulated Dyno curves in my models, close to the data for the Hacker 13.5, and I will try to explain my adjustments to the model using this analysis in a future post. For now I must examine the spreadsheet data a little more carefully and tweek my code to bring out more system variables.

PS - the purpose of a speed control is to moderate the average DC souce voltage Vs to a higher or lower "throttle position." Modern controls do this through Pulse Width Modulation (PWM). Lower Vs moves the air gap line toward the origin and allows the pilot to match the air gap power to the desired load power, for example, holding throttle constant in a low speed corner.
Attached Thumbnails
Novak Sentry as Brushless Dyno-motor_load_lines.png  

Last edited by SystemTheory; 03-17-2009 at 11:55 AM. Reason: added PS
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Old 03-17-2009, 02:20 PM   #86
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Good work ST. We are always open to hearing new suggestions, after all this is an open project.
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Old 03-17-2009, 07:46 PM   #87
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Thanks Matt, I appreciate the work you're doing, as I have wondered about the brushless system for a while now, and thought it would be good to have an open source dyno available in the RC or tech education community.

My prior load-line sketch is conceptually accurate except the number 2205 is not the correct intercept at the T = 0 axis. In the spreadsheet for the Hacker 13.5 this occurs at 7{s} with non-zero flywheel torque, so I've posted my adjustment to the line, based on extending the slope to the horizontal intercept.

The max power at the midpoint of this line peaks at 222{W}, and all I've done is assume a straight line for the Torque calculated by John and then extended to the final equilibrium. My calculations predict this final point should occur at 10.3{s}.

I'd like you guys to consider whether the data being cut-off early might impact the calculation of peak power in spreadsheet model. In Numerit Pro, the numerical derivative of angular speed appears to be sensitive to the extended speed and time in terms of coming up with a peak power value. I don't know if the spreadsheet includes a similar sensitivity.

My peak power points on the extended line:

Ts/2 = 0.1929{N-m}
wmax/2 = 1151{rad/s}
Pmpk = 222{W}

At this point when I plot a load line analysis on the extended line, I need to boost the start/stall current up to 110 Ampere to create equilibrium at the final speed of 2302{rad/s} with my red damping line passing through the torque-speed point at 7{s} and causing equilibrium at 10.3{s}. Then I get peak air gap power computed at 231{W} and bearing loss plus flywheel power adding up to 231{W}. I may sketch up the whole analysis tomorrow after I check my logic and calculations again.
Attached Thumbnails
Novak Sentry as Brushless Dyno-hacker13_5_extended.png  

Last edited by SystemTheory; 03-17-2009 at 08:14 PM. Reason: minor corrections
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Old 03-17-2009, 09:20 PM   #88
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Quote:
Originally Posted by SystemTheory View Post
At this point when I plot a load line analysis on the extended line, I need to boost the start/stall current up to 110 Ampere to create equilibrium at the final speed of 2302{rad/s} with my red damping line passing through the torque-speed point at 7{s} and causing equilibrium at 10.3{s}. Then I get peak air gap power computed at 231{W} and bearing loss plus flywheel power adding up to 231{W}. I may sketch up the whole analysis tomorrow after I check my logic and calculations again.
This logic is incorrect. There is no requirement that the damping pass through the flywheel torque-speed point at 7{s}, or at any other point. Rather, accepting the 10 Amp current sensor measurement as accurate at the 2205 speed point, I then tweek the starting current upward and plot the air gap line in a graph until equilibrium occurs at 2302{rad/s} with this logic:

tweek start/stall current up from sampled 106 Amps to assume Is = 116 Amps:

k = Ts/Is = 0.385/116 = 0.003319{N-m/A} and/or {V-s/rad}
w0 = Vs/k = 8.4/0.003319 = 2531{rad/s} ideal speed if there were no friction
D = (k*10A)/2205 = 1.505E-05{N-m-s/rad}

At Is = 116 Amps the load lines and air gap line look right. This causes equilibrium at 2302{rad/s}, the flywheel peak remains 222{W}, the predicted spin up time is 10.33{s}. I need to look into the total air gap power at the peak flywheel power (now estimated around 241-243 Watts in the air gap).

Last edited by SystemTheory; 03-18-2009 at 07:51 AM. Reason: minor corrections; clairity of variable "Is"
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Old 03-18-2009, 01:22 PM   #89
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I used cut and paste to put the exact time - speed columns from the Hacker13.5 spreadsheet into an engineering simulator. It takes a lot of hand time, since I must insert comma-separated values (csv) manually. If anyone knows how to save csv in Open Office Calc, please let me know?

Here are two plots of the actual speed sample data, the predicted speed, and my effort to generate a theoretical fit using the torque-speed line predicted in the spreadsheet at only two points:

Ts = 0.385{N-m}, w = 0
T = 0.016{N-m}, w = 2205{rad/s}

I think the curves show a very good fit of the predicted speed to the sample speed beyond the point labelled "5". The speed sensor deviates the most at the instant of turn-on up through approximately 1{s}/1000{rad/s}. After that it looks like a good match.

My formula for a theoretical speed is:

tau = 0.2*10.33{s} estimated time constant (from other sensed data)
wT = 2302*(1 - e^-(time/tau)) {rad/s} theoretical speed curve

This is a pretty close fit of the Dyno to a theoretical model. Error is less than 5% in most places above low speed.

John I think you're getting a good fit in the speed prediction and the sensor has limitations in the turn-on region. I am not sure how you're getting the angular velocity and predicted angular velocity, and would investigate any sources of calculation error or distortion in that process next.
Attached Thumbnails
Novak Sentry as Brushless Dyno-hacker_speed_fit.png   Novak Sentry as Brushless Dyno-hacker_speed_fit_07.png  
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Old 03-18-2009, 03:14 PM   #90
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"This is a pretty close fit of the Dyno to a theoretical model. Error is less than 5% in most places above low speed."

Its normal for people to get this backwards. That is not what you are doing nor is it what needs to be done. The Dyno data is measured data. Theoretical models can be fit to the data. You keep looking for errors in the measured data. Look elswhere. Look for errors in the theoretical model. Your last power number were too large. Its obvious the Sentry has a hiccup on starting up. It does not take a lot of high powered analysis. We could determine maximum power from about 10-15 points near the maximum with our method. The beginning and the end are not so important to us as the car rarely sees them.

If the theoretical model for power is linear in the parameters I can easily use excel to fit it to the data and determine the parameters of the model. I think you posted a power formula somwhere up above. I will take a look later.


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Last edited by John Stranahan; 03-18-2009 at 03:32 PM.
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