This blog has been created, in response to numerous requests, to document some of the stuff that I play around with. This will mainly be frames and engine parts for my own Aermacchi classic racing bike, but at times will also include the tools needed to make these parts. The initial posts will be looking rearward in time to lay the foundation for current and future work. There are more pix. on my Picasa page and web site at http://www.tonyfoale.com and http://picasaweb.google.com/tonyfoale
Thursday, 17 August 2017
Monday, 14 March 2016
Performance estimation. part 2 of 2
I can't believe that it was back in September that I posted the first part, I wrote this next part soon afterwards but forgot to post it. So here it is at long last.
In the first part we had a quick look at
some of the theory and difficulties associated with estimating the straight
line performance of motorcycles and other vehicles. This time we will look at the software, see how it works and work
though some examples.
As we saw last
time we can arrange the performance equation, F=ma to a =
F/m, we also noted some difficulties in specifying both the nett F
and equivalent m, which depends on inertia right back to the
crankshaft. Firstly let’s see how the
software arrives at values for F and a .
The nett F
is influenced mainly by engine torque and overall gear ratio, with aerodynamic
drag subtracting from this at higher speeds. Tyre rolling resistance also
reduces the value of F available but is reasonably constant
throughout the speed range and assumes relatively more importance at lower
speeds. There is also another effect
which reduces the average force applied through the tyre for acceleration which
is often forgotten, and that is the time that the torque is removed during gear
changes. Gear change times typically
range from 0.1 seconds for a very fast change with a quick shifter fitted to
around 1 second for a more leisurely foot movement. After the throttle closing and reopening during changing gears,
most engines require a certain time period for the fuel mixture to settle down
again before delivering full power, although modern EFI engines are much better
in that regard than older models. This
is not usually easy to quantify. The
first thing that we need to do in the software to start an estimation is to
enter the power or torque data, this will vary with RPM and we enter the data
into a table at appropriate values of RPM as shown in fig.1.
Fig.1 Data entry screen for
power/torque data. Either torque or
power numbers can be used and the software will calculate the other
appropriately. These curves are from my
own Suzuki SV650.
There is a “What
if?” option to allow the power curve to be increased by a given percentage
which gives a quick way of seeing the effect on performance of more or less
power. Once the power data has been
prepared I would normally move to enter data about the elevation of the road
surface, but as this is a virtual test on a perfectly flat and horizontal road
we can skip that step and proceed to the main data entry window shown in fig.2.
Fig.2 Main data entry
window. The graph is just a repeat of
the power/torque curves for reference.
The data entry boxes are for the multitude of parameters needed to get
the best performance estimate.
Working down the
left side. Initially, there is the
aerodynamic data. Looking at these in order:
CdA – this is a standard way of specifying the data from which to
calculate drag. The Cd is a coefficient
which puts a number on the efficiency of the shape regardless of size and A is
the frontal area which adds the size information. This value affects the top speed and high speed acceleration.
CP height – Centre of Pressure height. This is the height of the point
through which we consider the drag forces to act. At high speeds, the drag force creates a moment which lifts
weight off the front and transfers it to the rear tyre, thus creating more
potential traction. Aerodynamic load
transfer is also highly dependent on the shape of any fairing fitted which may
cause down force or lift, but without wind tunnel data we have little choice
but to ignore that factor. However, it
is at low speed in low gears when traction is needed most and so the effect of
this parameter is quite small and does not have to be particularly
accurate. This is especially true for
heavier and/or slower motorcycles.
Air density – Drag is directly proportional to air density. Fortunately, this is a value that is easily
calculated from temperature, barometric pressure and relative humidity. In our performance calculations I will use a
standard air density and so all virtual tests will use the same figure.
The next data
grouping is m (mass) or weight related, again let us consider
each in order;
CG height – The height of the centre of gravity. This parameter controls the load transfer, front to rear, due to
the acceleration. Up to a point this
transfer aids maximum traction and so if we have enough torque available, as in
the lower gears, it will aid acceleration.
The limit is if the load transfer is sufficient to unload the front
wheel completely leading to a tip over wheelie unless the applied torque is
reduced. The software automatically
calculates when a terminal wheelie is imminent and limits the torque to the
maximum usable.
Load on tyre,
front and rear – This is the static weight on each
tyre of the loaded motorcycle. This
gives us the mass of the bike without the rotary inertia inertia effects of the
wheels and rotating engine parts.
Wheel MoI,
front and rear – Moments of inertia of each
wheel. MCN now have the apparatus to
measure this.
Crank MoI – This is the moment of inertia of the crank and other engine
parts. This is difficult to measure without
an engine strip, but for the future I have asked the MCN testers to get the
dyno runs in at least two gears, from those I can make a calculation of the
whole drive train inertia.
Wheelbase
– This is obvious, but it is necessary for the performance calculations because
in conjunction with the CG and CP heights it controls the load transfer and
hence potential traction.
Next there is a
grouping of mainly tyre related parameters:
Rolling force – This is the force necessary to overcome friction and rolling
resistance of the tyres. It could be
measured by measuring the force to pull the bike along a flat tarmac surface,
but in most cases it will be estimated from published data on tyre
characteristics, as I mentioned last month.
Tyre maximum
µ – (µ is the symbol for coefficient of
friction) – This value is dependent on both tyre properties and the road
surface. For most purposes on dry
tarmac the value will be around 1.0.
Quality sports tyres may be around 1.1 and cheap noname tyres maybe as
low as 0.8 or worse. This figure will
only have a significant effect on our estimates for those motorcycles with
enough torque to spin the tyre. This is
rarely a problem in the higher gears and so top speed estimates will not be
affected but getting off the line on a sports bike will be highly dependant on
maximum µ, so low speed
acceleration calculations depend on how accurately we specify this number.
Peak rear
tyre slip – It is necessary for any tyre to slip to
a certain extent in order to produce a driving force. This not the same as the tyre spinning wildly such as when doing
a burnout, in that case the tyre is slipping much beyond the amount of slip
which produces the maximum drive. A
typical value of slip which produces the maximum traction is around 15%. That means that the tyre will be rotating
15% faster than necessary to match the road speed. The relationship between slip and driving force is extremely
complex and the software uses the so called “Magic formula” tyre model by
Pacejka which is commonly used in mathematical models of vehicle
behaviour. In common with the
coefficient of friction the value of peak slip will not affect top speed
estimates by much. However, at low
speeds the slip acts to effectively lower the gear ratio and this must be accounted
for in the calculations. Just as well
that these days we have computers to do the donkey work for us.
Tyre radius,
front and rear – This parameter for the front tyre
is used to calculate the angular or rotational acceleration of the wheel which
with the MoI of the wheel enables the programme to calculate the effective mass
of that wheel. The same applies to the
rear but in addition that tyre radius is used to calculate the relationship
between engine RPM, gear ratio and road speed.
The final data input
grouping on the left side specifies the testing requirements and conditions as
follows:
Maximum
distance – Within reasonable limits the maximum
speed of a vehicle depends on the length of the testing surface. The longer the test strip the higher the speed
that we can obtain. This parameter
specifies the cutoff length for our virtual test. There is an option to select ¼ mile length which is of course a
popular distance for acceleration testing.
Start
velocity – This was originally programmed into the
software for performance simulation on the race track so that the entry speed
onto a straightaway could be specified.
It could be used in our simulations to get rollon acceleration values.
Final
velocity and Include braking – Both of these
were also designed to be used for race track simulation and will not be used in
our performance estimations.
Head wind – The function of this is obvious but will not be used here. Our estimates will assume no head wind.
Moving over to
the top centre of the window we have a grouping of gear ratio data. This is information that is readily
available from owner’s manuals or other easily accessible sources and can be
entered with 100% accuracy. There is no
need to go into detail about this but the last two items need comment.
Gear change
time – This is the period that driving force from
the engine is removed during changes.
Typically it will range between 0.1 to 1.0 seconds. The actual time can have a very large effect
on acceleration as we will see in following examples, and is the motivator
behind Honda’s and Yamaha’s development of the so called seamless change gear
boxes used in the motoGP world championships.
RPM for
change – This is the RPM which we select to be when
we upshift. This determines which part
of the power curve we use. A low value
puts us lower down the power curve and the maximum potential acceleration will
not be reached, of course this reflects the reality of how we use our bikes
under normal riding conditions. Modern
bikes are too fast and accelerate too quickly to require riding techniques
which demand maximum use of the power available. Having said that it is also true that many people want to know
the maximum potential of their machines or of those that might represent a
future purchase. There is a lot of
misinformation around about the best RPM to change gear at to achieve maximum
performance, let’s consider a couple of options that get suggested.
Change gear at the RPM of peak torque – Of course this is based on a =
F/m, F is proportional to engine torque and so we get maximum
acceleration at the point of peak torque, right? Wrong, well it’s both right and wrong. It applies only if we are considering the acceleration in a given
gear. It is the torque at the wheel not
at the engine which determines acceleration and we can increase torque at the
wheel by simply using a lower gear and revving the engine more.
Change gear at the RPM of peak power – If we had an infinitely variable gear
box the maximum acceleration at any given speed will occur if the gearing is
set to give the engine RPM for peak power not peak torque. In practice we do not usually have
infinitely variable gear boxes and so we have a spread of RPM in each gear. For maximum acceleration we need to place
that RPM spread over the power curve such that the area under the power curve
is maximized. This will occur when the
peak power RPM is somewhere near the middle of our RPM spread depending on the
rate of increase or decrease of the power curve either side of the peak. So changing gear at the RPM for peak power
is also not the optimum, to enclose the maximum area we need to change gear
somewhere passed the peak. However,
there are further complications in the determination of the “exact” best
RPM to change at. One is because not
all gears in the box have the same proportional gap between adjacent gears, so
the RPM spread in each gear is likely to be different. Another is because in any given gear, the
acceleration is less at the high end of the RPM spread than at the lower
end. This means that we spend more time
at the high end of the spread and so it would optimize performance if that is
where the peak of the power curve was concentrated. In fact if we plotted the power curve against time instead of
against RPM then maximizing the area under that curve would truly give us the
optimum conditions. However, before we
can map the RPM based power curve onto a time based one we have to know the
performance of the bike first but that is what we are trying to calculate. A classic chicken and egg situation. If we wanted to go to such extremes we would
have to adopt an iterative approach.
That is; firstly make a guess at the optimum change RPM and calculate
the performance, then map the power curve to the time base and reevaluate the
change RPM and repeat the calculation.
Of course this would have to be repeated for each gear. In practice this would be going beyond
sensible limits to refine the values and placing the power peak between 2/3 to
¾ up the RPM spread will be very close
to giving the best performance, but before revving beyond peak power it would
be sensible to check the redline RPM for engine safety.
Fig.3 The RPM spread of 5^{th}
gear superimposed on the power vs. RPM graphs for gear change RPMs of 7250,
9200 and 9800.
Let us see just
what difference the gear change RPM value makes. Fig. 3 shows the RPM spread of 5^{th} gear superimposed
on the power curve for 3 different change RPMs. viz; 7250 which represents
changing gear on reaching peak torque RPM, 9200 for changing gear when peak
power is reached and 9800 which straddles the peak power RPM. Fig. 4. shows the
effect of these different change points on the velocity over time. Fig. 5 shows the effect on the distance covered
in the same time.
It is clear the
large difference between changing at peak torque RPM and near peak power RPM.
Fig. 5 shows
that when changing at 7250 it takes nearly a second longer to accelerate up to
500 metres. Fig. 4 shows that an extra 2 seconds is needed to reach
100mph. There is a much smaller
difference between changing on reaching peak power RPM and revving passed the
peak. For engine longevity it would be better to change at 9200 as the
performance penalty is minimal. The
power curves for this engine are fairly flat around the peak power area, on a
highly tuned engine the curve will be much steeper and the difference between
the 9200 and 9800 cases would be emphasized in comparison.
Top speed will
not be affected by the upchange RPM and so the velocity curves in Fig. 4 will
converge eventually.
Don’t forget to check out my web site at www.tonyfoale.com and buy the software .
Fig. 4 Plot of velocity vs. time showing the effect of
the upshift RPM. The green curve is for a change RPM of 7250, the blue is for
9200 and the red 9800 RPM. The 9200 and
9800 cases reach 100mph (160 km/h) in around 9.2/9.3 seconds but shifting at
7250 would take us 11.3 seconds or 2 seconds longer.
Fig. 5 Graph of distance covered when upshifting at 3 different RPM
values. It would take us another second
to cover 500 metres from a standing start with the early shift. However, engine life and fuel economy would
both be served better with the more gentle riding technique.
Thursday, 10 September 2015
Performance estimation. Part 1 of 2
F=MA
F=ma is probably the single most
important equation in everyday physics and mechanics. It describes all of our
physical actions and those of our motorcycles as well. So why are we discussing
it here? The answer will become apparent as we delve deeper into understanding
what makes our motorcycles perform as they do.
A few years ago
I wrote some software for simulating straight line performance. The motivation
was to help with gear ratio selection to optimize performance on a race
trace. It has proved useful in this
context and several race teams now use it.
Since then it has found a new and unexpected use. We are all familiar
with the performance road tests that most if not all car and bike magazines
feature with each new model, but have you ever wondered where the riders go to
ride at insane top speeds and burn rubber and clutches to get their
numbers? Some acceleration tests might
be done on a drag strip but a ¼ mile is not long enough to wind out to top speed,
at least 2 or 3Km is needed for that.
Even most race tracks do not have straightaways long enough. There are a
few special high speed test tracks in the world where you can get to and hold
top speed for as long as the tyres, machine and rider can take it. The problem with these tracks is that there
are very few of them, they are expensive to hire and are in constant use. What is the solution? It has been a fairly common practice for
magazines and their test riders to use a favourite section of public road which is both
reasonably flat and smooth, as well as being generally out of sight and with
little traffic. Such venues are getting harder to find with ever increasing
population and traffic.
Any modern
machine with even the minimum of
pretensions to being a sport bike will do 150mph and
several are pushing 200mph. With the
possible exception of the German autobahns those speeds are well in excess of
the maximum speed limits in any country. Obviously, that means that performance
tests carried out on public roads are without doubt illegal, not to mention
increasingly dangerous as bikes get faster.
Many magazines have been breaking the law and getting away it mostly up
to now. The editor of a US magazine, asked
me whether it was possible to make reasonable estimates of top speed and acceleration
with software. It just so happens that
a few years ago I developed some software for that very purpose. Many tests and comparisons since then have
shown that given the right information it produces figures which agree pretty
well with physical testing.
Engineers have
always tried to calculate the performance possibilities of whatever they might
be designing, be it bridges, ships, planes, cars or motorcycles. With the advent of affordable powerful
computers such calculations have reached a high level of sophistication over
the past few decades. Builders of
aircraft and other vehicles such as motorcycles have a very good idea of the
performance envelope of future models long before they leave the proverbial
drawing board. So how does it work?
To answer that
we return to the one single simple equation which answers all – yes it is F=ma.
To understand more let us look at just what it means. In words it can be expressed as Force equals Mass multiplied by
Acceleration. For our purposes it is acceleration
that is of most interest to us. If we
know the acceleration history of the motorcycle we can calculate its velocity
at any given point in time, which is exactly what we are after. So it makes more sense if we rearrange the
formula to give us the acceleration. It
then becomes a=F/m, that is; Acceleration equals Force divided by
Mass. This means that the acceleration
at any point in time is dependent of the nett force pushing the motorcycle and
the total mass of the motorcycle, including rider, fuel and luggage. Simple?
Well it would be if we knew the driving force over time and total
equivalent mass. Let us look at each of these terms, and some others, to
determine whether complications exist in the determination of these factors.

Velocity or speed.
Velocity put a number on how fast we are
traveling. In the metric system it is
usually specified as m/s (metres per second) or km/h (kilometres per hour) and
in the imperial system as ft/s (feet per second) or mph (miles per hour).
How velocity
varies over time is the essence of what our performance estimations are all
about. This what we want to know. All the calculations that we do, or get a
computer to do for us, are ultimately directed to this single parameter.
Acceleration.
Acceleration
tells us how quickly the velocity changes with time, either up or down. Although when the velocity decreases
(braking) the acceleration is often referred to as a deceleration, but is more
likely to be considered as a negative acceleration in calculations. Acceleration is expressed in units of
velocity divided by time or in the metric system as (m/s)/s or m/s² and
(ft/s)/s or ft/s² in
the imperial system. Another unit of
acceleration which is common to both measurement systems is g. This is a unit which compares acceleration
to that which gravity gives to a free falling object which is 32.2 ft/s² or
9.807 m/s².

An
example of an acceleration curve. The
short dips are due to the removal of driving force due to gear changes. Note how the acceleration decreases as the
speed increases as we change up through the box.

An important thing to understand about
acceleration is that it is not about velocity, it is about the “change”
in velocity over a given time period.
Consider as an example that we have an acceleration such that our speed
increases by 20Km/h over 1 second. Then
if we are traveling at 30 Km/h at the start of that second then at the end of 1
second we will be traveling at 30 + 20 or 50Km/h. However, if we were doing 200Km/h and experienced the same
acceleration for 1 second then we would end up at 200 + 20 or 220Km/h. In each case our speed changed by 20Km/h,
the starting velocity doesn’t affect that.
This leads us into how we can calculate
velocity over time if we have knowledge of how the acceleration varies with
time. This done by means of a
mathematical technique known as integration.
Analytically this is a continuous process but digital computers do not
work like that, they work in discrete steps.
We all know that acceleration of a vehicle is not constant over the
whole speed range from zero to maximum.
As we change to a higher gear acceleration reduces and even within a
single gear acceleration will vary depending on where we are on the power
curve. However, if we divide our period
of acceleration into much smaller time increments then within each of these
increments the acceleration will be close to being constant. The shorter the increment the closer the
acceleration will be to constant. This
prompts the question of just what time increment is appropriate for our
purposes. Modern sport bikes accelerate
very quickly, taking only a few seconds to go through the full range of the 5
or 6 gears. So obviously 1 second
intervals will be way too long for our calculations but might be fine for a
heavily loaded steam train. Whilst
developing my software I evaluated time increments ranging from a tenth of a
second to a thousandth of a second. I choose a period of one hundredth because
there was no significant change in the results by using a thousandth and it
reduced the number of individually calculations by a factor of ten.

This is the velocity curve which derives from the acceleration
curve above. Although gear changes
stop acceleration for short periods the effect on velocity is put small steps
in the velocity curve.

If we know our velocity at the start of any time interval
and acceleration history then we can calculate the new velocity at the end of
that time interval. We simply multiply
the average acceleration during the interval by the period of that interval and
add that to our initial velocity. If we
repeat this over the total period of acceleration then we will build up a
picture of how velocity varies with time.
Hence the importance of the expression “a=F/m”,
we need to calculate this as a precursor to calculating velocity.
Mass (also called inertia)
This is one of only two parameters needed to calculate
acceleration. “Mass is just the weight
of the bike – right”? Wrong! It is a little more complex I am afraid. Without going into the frequent
misunderstandings about the difference between mass and weight, let us consider
the complexities. In performance
calculations we are concerned with two types of mass or inertia. The most obvious is what can be called the
translational inertia and the less obvious one is rotational inertia. The word translation simply means a linear
or nonrotating motion. Rotational “inertia” is referred to as “Moment of
Inertia”, which I’ll abbreviate to MoI in the following text.
Just as it takes a force to accelerate an object in a
linear (translating) fashion it takes a torque or moment to accelerate a
rotating object. In order words if we
want to increase the spin rate of a wheel we have to apply a torque to it, in
order to accelerate its MoI. Imagine a
motorcycle wheel resting on the ground, now if we apply a horizontal force at
the axle we will start to accelerate the wheel along the ground but as well as
accelerating its mass along the ground we also have to accelerate its MoI in
rotation. Thus, the force that we apply
at the axle is not all available to accelerate the mass of the wheel in
translation, some of that force is split off to produce a torque to increase
the rotational speed of the wheel.
Looking at “a=F/m”
we see that reducing the force will reduce the acceleration. However, we can also reduce the acceleration
by using a higher value for mass in the formula.
There are several ways of dealing with the two types of
inertia in calculations but I find the simplest is to use the concept of an
“equivalent mass”. The equivalent mass
is a value for the combination of linear and rotational (or angular) masses
which gives the same results as if we calculated the proportional split of the
driving force needed for the rotational and translational accelerations. We might well ask how much difference
ignoring wheel rotational inertia makes
to our performance calculations, is it really significant? The answer depends on the parameters of each
individual model but a rough general guide is that without wheel MoI our
acceleration estimates would be high by over 10%.
Measuring the nonrotating masses of the motorcycle is
easy, we just put the machine and rider, ready to go, on some scales, but what
about the rotational inertia of the wheels?
There are no simple scales for that.
Well, there are several methods that could be employed to measure MoI,
which vary in difficulty and potential accuracy. The wheel MoI is important for reasons other than acceleration,
steering in general and leanin rate in particular are highly dependent
also. I won’t now go into how the MoI
will be measured, that will be the subject of a future article.
As I explained above, it is useful to convert MoI into an
equivalent translational mass, fortunately that is quite simple, we just divide
the MoI by the wheel radius squared.
Once we have done that for both wheels we just add those values to the
overall mass as determined on the scales.
Now we can modify our formula “a=F/m” to “a=F/me”
, where me is the equivalent mass. That is fine when both wheels are on the ground, but when
accelerating hard the front wheel may be airborne and so we should not add in
its rotational inertia until it touches down again.
If only things remained that simple. The crankshaft, clutch and other parts in
the drive train rotate and have to be accelerated as well. We are faced with problems getting accurate
data. Firstly, that sort of data will
be hidden away in the engineering files of the manufacturer and is not offered
in the sales documentation offered to the public or press. Unlike the relatively simple task of
measuring the MoI of the wheels, it just is not reasonable to expect to have to
dismantle engines and gearboxes to do the same with the innards. Modern sport bikes generally have small
diameter crankshafts and so compared to a wheel and tyre their MoI might be
small. However, engine components
rotate faster than the wheels by a factor equal to the overall gear ratio. That means that they have to be accelerated
faster also and that requires more torque, reducing that available for the
linear acceleration. Accounting for the gear ratio we can calculate the effect
of the engine components by adding an effective or equivalent MoI to the actual wheel MoI. Unfortunately, there is a square law
relationship between the true crankshaft MoI and its effective MoI when
transferred to the wheel. To see what
this means consider this example using the gear ratios from an Suzuki SV650 (I
just happened to have those on my desk).
In 6^{th} gear the overall gear ratio is 5.2:1, when we square
that we get 27. That means that we need
to multiply the crankshaft MoI by 27 to calculate its effect at the wheel. So even though the crank’s MoI may be
relatively low it starts to get significant when multiplied by 27 or so. It gets worse, the overall ratio of the same
bike in 1^{st} gear is around 3 times more at 15:1, with its square
equal to 225. The clutch spins slower
than the crankshaft and hence its effect is less, for the same motorcycle the
multipliers to use on the clutch MoI would be 6 when in 6^{th} gear and
51 when in 1^{st,} still quite significant multipliers. You can see why
some people lighten cranks and flywheels to increase acceleration.
The SV650 is in the middle of the range of crankshaft size
and the range of gear ratios. A large
cruiser Vtwin will have a much heavier crankshaft/flywheels but will be slower
revving with lower overall gear ratios which will tend to cancel out the effect
of the heavier crank. On the other hand
high revving multicylinder engines will have lighter cranks. So the MoI of the rotating engine components
cannot be ignored when making performance calculations.
Force
Force is the second of our two necessary
parameters. The engine produces a torque
which is transferred to the rear wheel after being multiplied by the overall
gear ratio along the way. The torque at
the wheel is resisted by generating a horizontal force at the contact patch of
the tyre on the road. That force is
what drives the bike forward, but it is not all available for acceleration,
firstly we have to deduct a bunch of parasitic losses. It is just like taxes, you earn $50,000 but
you are only left with $30,000 to $40,000 to put to good use. So the “F” in “a=F/m”
has to be the nett force after deducting tax.
At high speed
the most onerous tax is aerodynamic, that is air resistance, this is a tax on
speed. Tyre rolling resistance is a
base tax throughout the speed range but makes up most of the tax burden at low
speeds. Ground slope and wind can be
very important factors in determining the net force available for acceleration
but these can be ignored for our purposes if we are on a horizontal surface
with no head or tail wind. Tyre slip is
another factor that is very important, particularly in the lower gears. This detracts a little from the accelerating
force in the sense that air resistance does, and can also be considered as
putting a limit on the maximum possible driving force. Load transfer under acceleration increases
that limit.
Rolling
resistance is relatively easy to handle because tyre manufacturers do have
values for a rolling resistance coefficient.
Multiplying this coefficient by the loaded weight of the motorcycle will
give us the force that must be deducted
from the driving force. Typical
coefficients for motorcycle tyres are around 0.015 to 0.02 at low speeds,
depending on inflation pressure. That
means that a 250Kg loaded motorcycle needs around 5Kgf of push to move the
wheels around, if that sounds a bit low it is because when we move a bike about
we also have to push against chain and brake drag etc.
Information on aerodynamic drag for a
specific motorcycle is generally harder to obtain. Occasionally manufacturers will publish some data when they feel
it will be useful for sales, but in general this is rare. We are left with no alternative but to apply
some educated guesses as to what values to use in our calculations. Motorcycles tend to be grouped into distinct
performance/weight/size categories and within such groups the variation in drag
numbers is relatively small. Magazines
are a good source of performance data acquired from years of countless road
tests. So in the absence of a wind
tunnel the next best thing is to search for performance data from tests of
similar size and shape motorcycles.
Then we can reverse engineer those similar models in the software to
obtain aerodynamic characteristics that should be reasonably close to those of
the bike under consideration.
Torque/power curves (and how to measure them)
The starting base for determining the
driving force is the torque produced by the engine throughout the RPM range,
this can be measured by a dynamometer of which there are many types. The most common is known as an inertia
dynamometer. The rear wheel sits on a
heavy steel drum and the bike is ridden up through the gears as if riding on
the road. A certain gear is selected
for doing the actual measurement, typically 4^{th} or 5^{th} in
a 6 speed box, slower bikes will probably be done in their top gear. The “rider” will then accelerate the drum
throughout the required RPM range. A PC
together with some instrumentation will measure the acceleration of the drum in
small increments over the test duration.
This type of measurement has the advantage
that the acceleration of the drum is due to the torque on the rear wheel and so
transmission losses are inherently eliminated from our calculations, removing
at least one uncertainty. However, it
has the disadvantage that it does not directly measure torque, instead it
measures drum acceleration. The dyno
manufacturer knows the MoI of the drum and so he can say “To accelerate our
drum at this rate the torque had to be xxx”.
We have seen above that acceleration depends on wheel and engine
components MoI which varies with which
gear we are in. So in addition to the
drum MoI we really need to add in a value to account for the motorcycle’s
rotational inertias as well. Of course
your local dyno shop will not have that information for all the different bikes
that he gets to test. To make some
attempt to account for this, some dyno suppliers include what we might call
“fiddle factors” into their calculations which effectively add to the drum MoI. This inflates the power and torque figures
which the customer gets and so he goes away happy. This approach is not entirely without merit because if the fiddle
factor is accurate then we get power and torque curves without the effect of
engine inertias, which we know varies with which gear we are in. The problem is that there is no fiddle
factor that is applicable to all bikes in all gears on all dynos. There is no single drum size which is
optimal for the full range of motorcycles likely to be tested. In other words a simple drum inertia dyno,
although being a very useful tool is full of compromise and any results
obtained need to viewed in the light of such knowledge. However, there is a method using an inertia
dyno by which we can get better estimates engine MoI. I’ll elaborate on that in another article.
To summarize
In addition to the initial and current
use of the software for general performance calculation and gear ratio
optimaization, the increasing difficulty of economically and legally doing
actual performance tests has directed us to consider “virtual road tests”. Although the basis of such calculations is
as simple as “a=F/m” we have seen that there are various
complexities and uncertainties in the specification of both F and
m. That does not mean that we
are prevented from getting reasonable results.
Experience has shown that the software that I developed can produce
results for top speed and acceleration which match closely with practice. The next article in this series will look at
the software in detail and view various.
In the meantime you can see more details on my web site at www.tonyfoale.com
© Tony Foale August 2015
Saturday, 5 September 2015
Thursday, 9 July 2015
SEMINAR BARCELONA SEPTEMBER.
SEMINAR BARCELONA SEPTEMBER.
Over the past few years I have had a number of people asking me to give a motorcycle dynamics seminar within Europe. For various reasons this never happened. However, providing that there is sufficient interest I intend to give one during August or September in Barcelona. It will be a two day event and details of subject matter etc. can be found on my web site www.tonyfoale.com Email me on info@tonyfoale.com to express an interest and/or request more info. Also indicate any preferred dates and whether weekend or week days are better. Barcelona is a beautiful city with much to see and do so come and enjoy. BTW the seminar will be given in English. Please share this post.
Sunday, 21 June 2015
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