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Hydrogen-Boost December 2001 Newsletter

The Most Efficient RPM and Throttle Setting

    In a previous Hydrogen-Boost Newsletter article we had done an analysis on the efficiency of a vehicle’s engine while driving at various speeds.  That same analysis examined the mileage achieved and the possible mileage attainable at those various speeds.  Remember that we determined that an engine was much more efficient at producing work per volume of fuel consumed, when it was operating at higher power settings.  This only made sense because at low power settings the majority of the fuel being used was consumed in just keeping the engine running (idling).  At higher power settings this “wasted” fuel was a much smaller proportion of the total fuel used and so it would make sense that the engine would be more efficient.  Also, at higher power settings there would be more fuel/air compressed into the cylinder and this too would cause more efficient operation.  More discussion on that later. 
    In today’s tests we will compare the efficiency of an engine operating at full throttle but at various RPM’s.  What we are asking is this:  “When an engine is operating with the throttle wide open, is it more efficient at producing work per volume of fuel consumed, when it is operating at high RPM’s or when it is operating at low RPM’s.”  The answer to this question may surprise you.  Take a minute to think about your prediction to the answer to this question.  Think about why you think your answer is correct. 
    First I will describe the setup, observations, and calculations of the results of this experiment, and then I will discuss the reasons for the results.  The test vehicle was my 1994 Hyundai Excel 4-speed equipped with Hydrogen-Boost including a fuel heater.  I would suspect that the results would be the same in any vehicle.  The procedures of the experiment were as follows:  First it was determined at what RPM the vehicle operated at when it was in 2nd, 3rd, and 4th gears traveling at 15 mph and 40 mph.  Following this determination, repeated acceleration tests were recorded from 15mph to 40mph in each of the gears (2nd, 3rd, and 4th).  Times were recorded and averaged for each gear.
The data collected was as follows:

Speed        2nd  gear    3rd  gear    4th  gear   
15mph        2000 RPM    1320 RPM    1000 RPM
40mph        5000 RPM    3300 RPM    2500 RPM

Acceleration times from 15 mph to 40 mph
2nd gear    7.0 seconds
3rd gear    9.7 seconds
4th gear        12.0 seconds

    Now before doing any calculations, let us make some observations.  It is quite obvious that in second gear, at higher RPM’s, the engine produced greater power and thus shorter acceleration time.  But the question is not, when does it produce more power (work divided by time).  The question is when does it produce more work per volume of fuel used.  How can this be determined without fancy, expensive, equipment.  To do this let’s agree on a few things that may not be obvious to everyone.  The first is that at any given manifold vacuum reading the amount of fuel used per revolution will be the same regardless of the RPM’s.  If you don’t agree with this, think about it.  The EFI ECU (on board computer) adjusts the fuel/air mix to a set ratio, usually between 13-1 to 15-1.  Given the same vacuum reading, and thus the same absolute pressure, the same amount of fuel will be injected.  What makes the power output greater in 2nd gear is the fact that the engine is doing work faster at higher RPM than it would in 3rd or 4th gear.  But once again the question is which of those revolutions is doing more work per volume of fuel used?  The way we are going to calculate this is to determine how many revolutions it took to accelerate from 15 mph to 40 mph in each of the gears tested.  Now it must be noted that the work done in accelerating the vehicle from 15 mph to 40 mph is always the same but the extra work done in moving the vehicle a certain distance against road friction and wind resistance, will be different if the distance covered is different.  Also if the tests were not done on a flat road the work done in going up or down a hill will be different.  In our case the tests were done on a flat road and the distance covered in 4th gear was greater than the distance covered in 3rd or 2nd gears.  For now we will ignore the difference in work done because of the extra distance covered.
    Now the goal is to calculate the number of revolution for each of the accelerations.  To do this we will take the average RPM in each gear, divide by 60 second in a minute, and then multiply by the number of seconds in each acceleration.
2nd gear 2000+5000/2=3500RPM ave./60 sec. = 58.33 rev./sec times 7.0 sec.= 408 rev.
3rd gear 1320+3300/2=2310RPM ave./60 sec. = 38.5 rev./sec times 9.7 sec. = 373.5 rev.
4th gear 1000+2500/2=1750RPM ave./60sec. = 29.2 rev./sec. Times 12.0 sec. = 350 rev.
    So in considering only the work done in acceleration, we find that the engine is more efficient at converting chemical energy (fuel) into mechanical energy (work) when it is operating at full open throttle at low RPM’s.  So much for the rebuke of “lugging” the engine while driving, unless by lugging it is meant to throttle the engine so that it bucks and skips.  Here we have proven that during smooth acceleration above 1000 RPM’s the engine is at least 15% more efficient at an average of 1750 RPM than it is at an average of 3500 RPM.  If we compared the efficiency at 1000 RPM compared to 5000 RPM I would expect that figure to be more like 30%.  Remember that this is not even figuring in the extra distance traveled during the low RPM test. 
    What does this all mean to us as maximum mileage experimenters?  It means that it is more efficient to accelerate at heavy throttle and low RPM than it is to accelerated at the same rate with medium throttle and higher RPM.  Some of us have been taught that this type of driving will carbon up the cylinder and the head and valves.  This may have been true with older vehicles equipped with poorly adjusted carburetors, but with EFI equipped vehicles with Hydrogen-Boost installed it should not be a problem.
    Now let’s discuss why an engine is more efficient at low RPM’s.  First let us discuss the combustion process in an internal combustion engine.  A typical internal combustion engine fires the spark plug at 10-15 degrees before top dead center.  This is because the combustion process is so slow, that as the piston is pushed down the cylinder the fuel doesn’t have time to combust completely.  Combustion is always easier at higher pressures, and if we can slow the piston down so we can keep the pressures higher, for a longer period of time, we can get more of the fuel to completely combust at the top of the power stroke where it actually does some good.  Once the piston is more than one third of the way down the cylinder it is moving faster than the pressure can push it down so no work is done in the latter two thirds of the power stroke.  So if we want efficiency, we drive at low RPM’s and high throttle settings, then when we don’t need to accelerate we coast with the engine off, except when we have an automatic transmission.  I know this last statement will be controversial and it is a reference to even more controversial porpoising technique discussed in an earlier newsletter.

Follow Up Verification

    The following day I designed an experiment the results and conclusions of this experiment.  This time the test was not an acceleration test at constant throttle setting, but a constant power setting (work divided by time) at various throttle settings in three gears.  The vehicle used for this experiment was the Geo Metro XFI 5-speed equipped with Hydrogen-Boost including fuel heater.  Some initial calculations had to be made to determine the RPM’s during each test because the Geo is not equipped with a tachometer.  This determination was done by observing the speed the vehicle would travel at 1000 RPM’s (idle).  To do this the car was accelerated to a speed greater than the approximate speed known to be the idle speed in each gear.  Then the clutch was depressed and released several times until there was no deceleration noticed when releasing the clutch.  The speed was noticed and a repeat of this procedure was done from below the given speed.  This time when the clutch was released there was a slight acceleration.  When the speed was found at which there was no acceleration nor deceleration, this was recorded as the speed of the vehicle at 1000 RPM.  This was done for each gear with the following results:

Gear        1st    2nd    3rd    4th    5th
Speed (mph)    6    11    16    21    26

From this data I could calculate the RPM’s at any speed in any gear, in this case 25 mph.

Gear        1st    2nd    3rd    4th    5th   
RPM’s      4166    2273    1563    1190    962

    The experiment was conducted as follows:
A hill was found in town that had little traffic anda place to turn around on top and at the bottom.  This hill was long enough and with constant enough pitch that it could be determined at what manifold vacuum reading the vehicle could maintain constant speed going up the hill in each of three gears (1st, 2nd, 3rd) at a constant speed of 25 mph.  From the manifold vacuum setting, the absolute pressure was calculated by subtracting the vacuum from 30” (atmospheric pressure).  The fuel index was calculated by multiplying the absolute pressure by the RPM’s  because the fuel injected is proportional to the absolute pressure of the air in the intake.
The following was the average of several tests in each gear:
Gear            1st        2nd        3rd        4th(estimated)
Manifold Vacuum    12”        8”        3”        -3”
Absolute pressure    0.6        0.733        0.9        1.1 atmospheres
Fuel index        2500        1667        1407        1309
    Conclusions drawn from this experiment are consistent with the previous experiment except that in this experiment we do not have to ignore the work done by pushing the car down the road.  So the results of this experiment should give us a more accurate estimate of the relative efficiency of the engine at various throttle settings.  One thing that this experiment does not do is compare the efficiency of the engine at the same throttle setting and different RPM’s.  All things considered we can indeed make the following conclusion:  It is more efficient (by far) to accomplish a given amount or work (25 mph of this hill) when we do so in the highest gear (lowest RPM) that the vehicle can use to accomplish the task.  In fact in fourth gear we used a little over half the fuel used in first gear.  This is probably no surprise to anyone. 

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