Best RPM for most efficient fuel consumption.

[Edward Hayes]

There are two different terminologies here that are totally
different. One is maximum engine efficiency which is directly measured
by the amount of HP produced per amount of fuel consumed i.e. brake
mean effect pressure in the cylinder and this occurs at or very near
the maximum torque. The other measurement is maximum gas mileage which
is a function of engine design and vehicle characteristics. I can
assume that the maximum gas mileage for my Subaru occurs at the torque
converter lockup rpm which is about 1700 rpm and ~ 37 mph.

 

[Mike Lloyd]

Plus the A/C take about 5HP... The alternator takes some more, esp if you
have 350W worth of stuff plugged in as one guy does (refer to the alternator
post going on right now too). Add some more stuff for power steering and
smog devices and then you've got more loss.

 

[Carl 1 Lucky Texan]

Just an honest question here : if it takes 34 hp to go 80 mph, what is
my engine doing with the other 100 hp it has in reserve? I only tap into
it when accelereating? TIA.

Those numbers come close to agreeing with a test Serge Scherbatskoy (a
consultant where i used to work) did in his old pickup truck. He built
an accelerometer and went 2 directions on the highway at 55mph. He took
his foot off the accelerator and his device captured the instantaneuos
deceleration. he got 12hp for his number.(I asked the same question you
did, the other hp is used fighting inertia) It was some old full size
truck, no cap, I guess tailgate up, etc. I think edmund scientific may
have a gizmo that does this so , if you're better at math than me, you
could figure it out for yourself. Since Serge worked on the Manhattan
Project and even shared a room with Enrico Fermi - I guess it was easy
for him!

Carl

 

[Carl 1 Lucky Texan]

Forgot to add a constant 5 HP *load* to show what
that does-

MPH HP MPG MPG(HP+5)
10 0.6 273 29
20 1.6 204 49
40 5.9 111 60
60 15.8 62 47
70 23.7 48 40
80 33.9 38 33

More data points from your table would be interesting to
see to show where the actual peak MPG is for various parasitic
losses.

thank you - this is a fun exercise!

Carl

 

[Bruce Hoult]

Forgot to add a constant 5 HP *load* to show what
that does-

MPH HP MPG MPG(HP+5)
10 0.6 273 29
20 1.6 204 49
40 5.9 111 60
60 15.8 62 47
70 23.7 48 40
80 33.9 38 33

More data points from your table would be interesting to
see to show where the actual peak MPG is for various parasitic
losses.

Thank you for holding up my end of the argument while I was away for a
weekend ski-trip

Those figurs are clearly much better than we get from our actual cars,
so if there is a constant "load" or loss somewhere to add to the
aeerodynamic drag then it must be higher than this. How much higher?

I don't know figures for fuel consumption per hp, but by
reverse-engineering your results I get MPG = 16.35 * MPH/HP.

I think it gets very interesting if you work out the numbers for HP+20
(i.e. asssuming 20 hp losses in engine, drivetrain etc):

MPH HP MPG MPG(HP+5) MPG(HP+20)
10 0.6 273 29 7.9
20 1.6 204 49 15.1
40 5.9 111 60 25.3
60 15.8 62 47 27.4
70 23.7 48 40 26.2
80 33.9 38 33 24.3

Empirically, this looks pretty darn close to the sort of mileage (US
mpg) a lot of us get out of our Legacy's at constant speeeds on the open
road. (for non-US people, those numbers are 9.5, 18.2, 30.3, 32.9,
31.4, 29.1 mpg)

Note that the most economical speed is 60 mph, not 40 mph. And in fact
70 mph is 4% more economical than 40 mph! (and 80 mph is only 4% worse
than 40 mph!)


Here is another cross-check. Earlier this year I spent several weeks
driving a Ford Territory around suburbs at as close to a constant 40
km/h as wee could manage (measuring 3G mobile phone data rates for
acceptance testing by a telco). Over that time, according to the trip
computer, we averaged 21 l/100km (13.5 mpgUK, 11.2 mpgUS). At one point
I was able to drive at a very steady 110 km/h (70 mph) for 60 or 70 km
on a straight & flat road and it acheived 12 l/100 km (23.6 mpgUK, 19.7
mpgUS). That's a ratio of 1.75 between the two speeds. Looking at the
numbers above, we see a ratio between 70 mph and 20 mph of 26.2/15.1 =
1.735. That's very much in line with each other.

 

[JohnO]

I think it gets very interesting if you work out the numbers for HP+20

(i.e. asssuming 20 hp losses in engine, drivetrain etc):

MPH HP MPG MPG(HP+5) MPG(HP+20)
10 0.6 273 29 7.9
20 1.6 204 49 15.1
40 5.9 111 60 25.3
60 15.8 62 47 27.4
70 23.7 48 40 26.2
80 33.9 38 33 24.3

My math isn't up to par here, but the data point that would fall at 50 MPH
would seem to be important on this curve. (big gaps in the data, and the
speed falls directly into the range in question) And, if you do HP+30, I'm
sure your number might show the best mpg is at 75...IOW you could factor
this into anything you want. ;-) There's no way the car chews up 20 hp
internally anyway...it moves when I let go of the brake at idle, when I'm
generating what...a couple hp?

-John O

 

[Mike Lloyd]

I agree. I think there is much less than a 5 hp loss from piston to rubber.
20 at a minimum, and then it goes up from there. Look at a typical
motorcycle magazine -- they will often compare RWHP (rear-wheel hp) to crank
HP and the difference is much larger than 5. Hell, even on a motorcycle it
can be as much as 20 hp, and those things are a lot less complex (well, they
used to be anyway!) and have much less accessories like A/C and stereos
systems to drive (minus the gold wing, but hell, that bike even has
reverse!).

mike

 

[Mike Lloyd]

I meant much *more* not less. But I see where JonO is going. To do this
correct you'd need real numbers, both RWHP and rank HP from a car, with
known consumption rates to back up the math. But I seems like we are for
sure headed in the right direction.

I agree. I think there is much less than a 5 hp loss from piston to
rubber. 20 at a minimum, and then it goes up from there. Look at a typical
motorcycle magazine -- they will often compare RWHP (rear-wheel hp) to
crank HP and the difference is much larger than 5. Hell, even on a
motorcycle it can be as much as 20 hp, and those things are a lot less
complex (well, they used to be anyway!) and have much less accessories like
A/C and stereos systems to drive (minus the gold wing, but hell, that bike
even has reverse!).

mike

 

[Bruce Hoult]

I think it gets very interesting if you work out the numbers for HP+20
(i.e. asssuming 20 hp losses in engine, drivetrain etc):

MPH HP MPG MPG(HP+5) MPG(HP+20)
10 0.6 273 29 7.9
20 1.6 204 49 15.1
40 5.9 111 60 25.3
60 15.8 62 47 27.4
70 23.7 48 40 26.2
80 33.9 38 33 24.3

My math isn't up to par here, but the data point that would fall at 50 MPH
would seem to be important on this curve. (big gaps in the data, and the
speed falls directly into the range in question) And, if you do HP+30, I'm
sure your number might show the best mpg is at 75...IOW you could factor
this into anything you want. ;-)[/QUOTE]

Well, yes and no. it's true that if you try HP+32 (30 isn't quite
enough) then 70 mph takes the lead as the most efficient speed. The
problem with that is that it's only 20.5 mpgUS (24.7 mpgUK) which is
well under the numbers we actually see from our cars at those speeds.

There's no way the car chews up 20 hp internally anyway...it moves
when I let go of the brake at idle, when I'm generating what...a
couple hp?

You only have a few surplus hp at idle -- that is, power available to
move the car -- but how much is being chewed up in addition in internal
friction and also in driving the alternator and aircon compressor?
Aircon on makes a very noticable difference to the acceleration or hill
climbing ability of cars with engines under about 1500cc so that must
take quite a bit of power. And yet the engine can power it at idle.

If the car *doesn't* chew up 20 hp internally then why don't we get 50 -
60 mpg? Or at least 40 - 45?

 

[Larry Van Wormer]

I meant much *more* not less. But I see where JonO is going. To do this
correct you'd need real numbers, both RWHP and rank HP from a car, with
known consumption rates to back up the math. But I seems like we are for
sure headed in the right direction.

It's a percentage loss, not a specific quantity, at least to a good
approximation. An adequate reference is at:

http://www.sdsefi.com/techdyno.htm

It states that a typical loss through the drive train is around 12%,
which seems to match fairly well with other references I've seen. So, if
the required horsepower for the speed is 20, the power output required
from the motor is about 23, rounded off.

 

[Mickey]

so to take your table,
here is an illustration of how high the engine, drivetrain
and other losses are-
If you take the HP and convert it to gallons per second
consumption and then use the MPH to get miles per second -
divide miles per second by gallons per second and you get the
MPG if all other losses did not exist. It shows why for
slower vehicles, the other losses are so significant.

MPH HP MPG
10 0.6 273
20 1.6 204
40 5.9 111
60 15.8 62
70 23.7 48
80 33.9 38

Which is why vehicles designed to run maximum MPG for
demonstration purposes are slow speed,
with all the other losses attacked to
try and reduce them to minimum.

The throttle of course controls the horsepower output. The engine is only
being asked to provide 34 HP by your right foot. If you ask for more
power, you accelerate.

You've not indicate how you arrived at those figures but it appears
you are assuming 100% energy content of the fuel is used to move you
down the road. Thermal efficiency of a gas internal combustion engine
is on the order of 25% with the remaining energy being lost in the
form of heat, cooling system, exhaust, radiation etc.

Mickey

 

[Mickey]

...
It states that a typical loss through the drive train is around 12%,
which seems to match fairly well with other references I've seen. So, if
the required horsepower for the speed is 20, the power output required
from the motor is about 23, rounded off.

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The spreadsheet I use and sighted in prior post was taking into
consideration drive train efficiencies of 85%, not far off from the
12% sited above. Mech drive are about 90-95% efficient. If one were
to assume the 95% figure and factor in trans, engine and differential,
the 3 combined figures would equal 85%.


Rounded to nearest one place.
speed air rolling total total + engine
mph HP HP HP HP
10 0.1 0.6 0.6 0.7
20 0.5 1.1 1.6 1.9
30 1.6 1.7 3.2 3.8
40 3.7 2.2 5.9 7.0
45 5.2 2.5 7.8 9.1
50 7.2 2.8 10.0 11.8
55 9.6 3.1 12.7 14.9
60 12.4 3.4 15.8 18.6
70 19.7 3.9 23.7 27.8

Here is the data used in the calc

Assume Cd = 0.5 head wind, mph = 0 G = Grade, percent width = 5.5
height = 4.5 V = Velocity, mph
then Area = 24.75 ft^2 W = GCVW, lbs
air drag hp = 4.65E-006*Cd*A*v^3
Assume mechanical efficiency = 0.85
Assume Crf (CoF of rolling resistance)= 0.006
grade hp = .002933*G*V*W
rolling friction hp = Crf*V*W*(5280/1.98E06) if W = 3,500

Unlike some assume, weight doesn't play a big part. If I dropped the
weight 500 lbs the rolling drag only dropped by .5 HP.

It's all about WIND RESISTANCE. Add a 20 mph headwind to the above
figures and at 60 mph you go from 15.8 HP to 32.8 HP


Mickey

 

[Larry Van Wormer]

The spreadsheet I use and sighted in prior post was taking into
consideration drive train efficiencies of 85%, not far off from the 12%
sited above. Mech drive are about 90-95% efficient. If one were to
assume the 95% figure and factor in trans, engine and differential, the
3 combined figures would equal 85%.


Rounded to nearest one place.
speed air rolling total total + engine
mph HP HP HP HP
10 0.1 0.6 0.6 0.7
20 0.5 1.1 1.6 1.9
30 1.6 1.7 3.2 3.8
40 3.7 2.2 5.9 7.0
45 5.2 2.5 7.8 9.1
50 7.2 2.8 10.0 11.8
55 9.6 3.1 12.7 14.9
60 12.4 3.4 15.8 18.6
70 19.7 3.9 23.7 27.8

Yep, all of that makes good sense. Then, when combined with the gasoline
engine pumping losses (smaller throttle openings yield less efficiency),
it is usually true that the best fuel mileage for a vehicle occurs at
the lowest speed at which top gear can be used. (lowest engine
rpm/friction loss, and greatest throttle opening for the required output)

Of course, that's usually too low a speed to be practical for most
highways...

 

[Dave - Dave.net.nz]

Okay, fair enough, I accept that can occur. Any data available as to how
much of the total drag this component is likely to make up?

(I've found this interesting. The various references seem to leave it
clear: For a specific vehicle, the lowest speed that can be maintained
in top gear is most likely going to give the best fuel economy, because
engine efficiency is thus maximized (lower pumping losses, mainly) and
oeverall drag is minimized.)

personally I travel at ~80km/h when no traffic is around... if I notice
that somethings coming from behind, I speed up to 100km/h, at 80km/h I
get almost 7.5l/100km, at 100 it is closer to 9l/100km.

 

[xmirage2kx]

My math isn't up to par here, but the data point that would fall at 50 MPH
would seem to be important on this curve. (big gaps in the data, and the
speed falls directly into the range in question) And, if you do HP+30, I'm
sure your number might show the best mpg is at 75...IOW you could factor
this into anything you want. ;-)

Well, yes and no. it's true that if you try HP+32 (30 isn't
quite
enough) then 70 mph takes the lead as the most efficient
speed. The
problem with that is that it's only 20.5 mpgUS (24.7 mpgUK)
which is
well under the numbers we actually see from our cars at those
speeds.

There's no way the car chews up 20 hp internally anyway...it moves
when I let go of the brake at idle, when I'm generating what...a
couple hp?

You only have a few surplus hp at idle -- that is, power
available to
move the car -- but how much is being chewed up in addition in
internal
friction and also in driving the alternator and aircon
compressor?
Aircon on makes a very noticable difference to the
acceleration or hill
climbing ability of cars with engines under about 1500cc so
that must
take quite a bit of power. And yet the engine can power it at
idle.

If the car *doesn't* chew up 20 hp internally then why don't
we get 50 -
60 mpg? Or at least 40 - 45?
[/QUOTE]

this doesnt take any real math to figure out. my escort gets its best
milage at 50mph my concorde gets its best milage at 65mph. and yet
still a pruis gets its best milage between 10-15mph with multi stops.
there is no golden speed that if we all travel at we get the best
milage. its as simple as: the best mpg is gotton when your car travels
the most miles on the least gas. all the math in the world wont really
help you because there is to mch to take into account, air pressure,
incline, road surface, weight, physical location on the globe, temp,
elevation, etc, etc, etc. and just forget about the car itself,
current oil displacement, tire pressure, tire tread, gearing, etc,
etc, etc, etc, etc, etc. I could fill a dictionary sized book with
just the lists of things you would have to take into account, plus you
would have to take it all into account atleast every tire rotation. to
have any real arguement you have to use the KISS rule (keep it simple
stupid)

 

[JohnO]

There's no way the car chews up 20 hp internally anyway...it moves

You only have a few surplus hp at idle -- that is, power available to
move the car -- but how much is being chewed up in addition in internal
friction and also in driving the alternator and aircon compressor?
Aircon on makes a very noticable difference to the acceleration or hill
climbing ability of cars with engines under about 1500cc so that must
take quite a bit of power. And yet the engine can power it at idle.

If the car *doesn't* chew up 20 hp internally then why don't we get 50 -
60 mpg? Or at least 40 - 45?

Wind resistance? Maybe it's that air scoop on the hood, of the fog lamp
sockets. <g> Ahhh, whatever. On my way in to work today, I was driving 47
mph at about 1600-1700 rpm. The engine is barely working, and I'd love to be
able to drive at this speed for a couple hundred miles to see what happens.

-John O

 

[Edward Hayes]

My Forester ATs torque converter locks up at ~ 1,700 rpm which is ~37
mph. I assume that this is a value that Subaru has chosen that allows
the engine to NOT lug but, is at or near the lowest rpm that will
produce a good mileage figure. I would guess that very close to 40 mph
is the speed at which I get the best mpg and the chart reflects that
value closely. I also did some gas mileage measurements on a long 3500
mile trip. Fuel consumption was measure for 3 complete fuel fills
(~1000 miles ) with air on 100% ( yes compressor cycled) and close to
1000 miles with air off and window open. The difference in gas mileage
and HP loss due to the air conditioner was 1.96 hp. However my
Forester will consistently yields 27.6 mpg at 72 mph with the air on.
This is one interesting mental exercise. Thanks Ed

 

[Edward Hayes]

I wish my Forester was geared to run 47 mph at 1700 rpm. Mine is
running only 37 mph at 1700 rpm.

 

[JohnO]

I wish my Forester was geared to run 47 mph at 1700 rpm. Mine is running
only 37 mph at 1700 rpm.

I have to get up to about 53 mph first, and then back into ~45. That's about
as slow as I can go without the trans shifting to a higher gear.

-John O

 

[Andy Leszczynski]

I own a 2003 5 speed manual outback. I usually run my tacho at 3200 to
3500 RPM. Is this in fact the most efficient rpm for the engine? I
know that typically once you go over 110 kph fuel efficiency drops but
it depends on what rpm the engine in running at the point where most
horsepower is put out without consuming too much fuel.

Any thoughts on this?

Paul

Thx for the topic and a lot of interesting knowledge. I was wondering
what is the function MPG(MPH) too for long time. I will add 2c too,
something was surprised me about year ago. My wife took het Imreze 2.5TS
and went alone around the half USA about year ago. Chicago-New
Orleans-Mexico Gulf-Texas-New
Mexico-Arizona-Nevada-Arizona-Utah-Colorado-Nebraska-Chicago) trip
yields 10k miles. I flew in and we met in Las Vegas and drive back to
home together.

I was observing the MPG for long time and at speeds 80-90 MPH we were
getting about 25MPG. Once we went into the Colorado mountains the MPG
raised about 2MPG yet having similar speeds. I was shocked – I thought
the mountains should affect MPG negatively. I do not have an
explanation, but I kind of think it is due to more efficient engine
works, at full throttle and full torque, what is often a case in mountains.


A.