<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<!-- saved from url=(0053)http://members.cox.net/bdfelice/Ackerman/ackerman.htm -->
<HTML><HEAD><TITLE>ackerman</TITLE>
<META http-equiv=Content-Type content="text/html; charset=iso-8859-1">
<META content="Brian D. Felice" name=Author>
<META content="MSHTML 6.00.2800.1476" name=GENERATOR>
<META content="blends 011" name="Microsoft Theme"></HEAD>
<BODY text=#000000 vLink=#0000ff aLink=#ff9900 link=#993300 bgColor=#cccccc
background=ackerman_files/blegtext.gif><!--mstheme--><FONT
face="Trebuchet MS, Arial, Helvetica">
<BLOCKQUOTE>
<BLOCKQUOTE><FONT face="Times New Roman" size=3> Ackerman-
what it is, what it does and why we care.</FONT>
<P><FONT face="Times New Roman" size=3> A short
history: In the early days of automobiles, no one could make a (4)
wheel car steer correctly. Cars were often driven on wooden floors in the
early days (demonstration purposes only- they were not yet practical anyway)
and the versions with 4 tires were always leaving rubber marks behind. Tire
life was terrible and the cars would often buck as they were turned; this is
why there were so many three wheeled cars initially. The problem was known-
as a car is driven in a circle, the inboard front tire (assuming it is front
wheel steering) must make a smaller turning radius than the outside front
tire. This is evident from tire tracks after a snowfall, a car turning in a
circle will leave two distinct circles, one smaller than the other. This was
not an easy problem to fix because each tire will be the inside the circle
at some time and as the turning radius is changed, so too must this
differential change with it. Enter one Mr. Ackerman- he proved his geometry
using bedroom doors and a piece of string. Much later in time this principle
was applied to automobiles. Sure enough, it works perfectly. All cars since
that time have Ackerman built into the steering wheels as a necessity
and it is not subtle; turn the wheels to full lock on any car (while
stopped, of course), step in front of the car and note the direction the
tires are facing. The inboard tire will be turned significantly further than
the outboard tire; reverse the direction of the turn and Ackerman reverses
also.</FONT>
<P><FONT face="Times New Roman" size=3> Ackerman is rotary
to linear differential. For those who know what a cosine curve looks like,
Ackerman simply moves the link between rotary movement away from X = 0. The
most intuitive example of Ackerman, at least to me, is any piston engine.
Notice that while crankshaft speed is constant, piston speed constantly
changes from maximum near 90 degrees to <zero> speed at the top and
bottom of the stroke. This is also the Ackerman principle at work.</FONT>
<P><FONT face="Times New Roman" size=3> I must confess to
misusing the term. Ackerman is the specifically the geometry found on the
steering end of cars. I have applied it to the control surfaces of model
planes erroneously- it's a misnomer. However, I can't think of another word
that describes it so well.... </FONT>
<P><FONT face="Times New Roman" size=3> For a visual
example, look at the circle below: <IMG height=441
src="ackerman_files/Acker-1.jpg" width=630> </FONT>
<P><FONT face="Times New Roman" size=3> This drawing shows
two symmetrical points, each offset 15 degrees from the centerline, or
15 degrees away from 90 and -90 degrees. This is how Ackerman is introduced
into our control systems. When this wheel is turned, anything attached to
these points and held at -0- degrees (horizontal) will not move the same
distance. See below:</FONT>
<P><FONT face="Times New Roman" size=3><IMG height=438 hspace=85
src="ackerman_files/Acker-2.jpg" width=491> </FONT>
<P><FONT face="Times New Roman" size=3> And here it is in
a nutshell- Ackerman has made the linear distance different between the top
and bottom. Notice that the wheel was rotated 15 degrees, and the top linear
distance was 0.113 inches but the bottom distance is only 0.105 inches. This
is what Ackerman does. Ackerman is dependent on the initial angles chosen-
if +/- 90 degrees are chosen (that would be the top and bottom center of the
circle), there is no Ackerman introduced and all linear motion will be the
same for both points. The angle that will generate max. Ackerman is 45
degrees. This examples uses 15 degrees so that it's easy to see but in
practice, we would normally choose something more reasonable for a pull-pull
system....</FONT>
<P><FONT face="Times New Roman" size=3> The reason
Ackerman works as it does is because any point attached to a disk that
rotates makes both horizontal and vertical motion. In other words, a clevis
attached to a rotating control arm will move both back and forth, but also
up and down. What Ackerman does is alter this relationship; using Ackerman,
we 'trade' some of our fore-aft movement for up-down movement, which we
don't care about. This is exactly where the slack comes from..... the cable
going slack is doing so because it's also moving closer to the pivot point
(on a horizontal line). If this is not clear, try to visualize the movement
that occurs between the two drawings above; the upper cable is moving a
greater distance left - right than the lower cable is but the lower cable is
moving a greater distance up - down than the upper cable is. Effectively, we
are trading this up - down motion, which we don't care about, for a
differential left - right motion, which we certainly do care about.</FONT>
<P><FONT face="Times New Roman" size=3> The next part in
understanding the application of Ackerman is seeing where this circle and
connection points is found on our toy planes. It would initially appear that
there are no circles used as all we use are servo arms and surface control
horns but this is not quite true as a circle can be drawn around any three
points. This means that there really is a circle around both the servo arm
and the control surface. As most servo arms are straight and therefore
symmetrical, we can't easily introduce Ackerman at the servo end of the
system so it has to be used on the 'other' end of the system. Look at the
next picture for a visual reference as to how and where Ackerman is
introduced into our toy planes. <BR> </FONT>
<P><FONT face="Times New Roman" size=3><IMG height=442
src="ackerman_files/Acker-3.jpg" width=758> </FONT>
<P><FONT face="Times New Roman" size=3> This is a typical
control arm installation. We can draw a circle using the hinge line as the
center, and sweeping right through the holes that the clevises (clevi?)
attach to. The red line is shown for reference between the holes in the
control horns. This drawing isn't the best but the forward flat part would
represent the horizontal stabilizer, the aft portion would be the elevator,
and the horns / clevises are shown mounted directly above and below the
hinge line. This mounting scenario has NO ACKERMAN. It is fully symmetrical
and will be absolutely linear. As one cable moves rearward, the other cable
moves forward the identical distance.</FONT>
<P><FONT face="Times New Roman" size=3> The next view
should make Ackerman usage clear: <BR> </FONT>
<P><FONT face="Times New Roman" size=3><IMG height=432
src="ackerman_files/Acker-4.jpg" width=707> </FONT>
<P><FONT face="Times New Roman" size=3> The horns have now
been moved rearward 0.140 inches in relation to the hinge line. Note the red
lines- these indicate the angle formed between the horn holes and the hinge
line. As the bottom cable moves forward to deflect the flight surface
downward, the upper cable will move rearward but NOT AS MUCH as the bottom
cable moves forward. It is a distinctly asymmetrical system. This is also
positive Ackerman; moving the holes in the control horns forward would
create negative Ackerman, and this would be disastrous.</FONT>
<P><FONT face="Times New Roman" size=3> Now watch what
happens when this system is deflected:<IMG height=431
src="ackerman_files/Acker-5.jpg" width=734> </FONT>
<P><FONT face="Times New Roman" size=3> The control
surface has been deflected 10 degrees but the cable travels are not equal-
there is a .004" (inch) difference between the upper and lower cable
movement. This will introduce exactly that amount, 0.004", into the
non-pulling side of the cable, which is the upper cable in this case. Of
course if the deflection is the other way (up), then the differential will
also be the other way.</FONT>
<P><FONT face="Times New Roman" size=3> It also does not
matter which side has the slack- as the airflow will always force the
deflected surface toward the neutral position, the nature of the forces
involves actually chooses which cable is taut and which is slack.</FONT>
<P><FONT face="Times New Roman" size=3> One other critical
consideration: The pull-pulls must be centered around the hinge line rather
than some other geometry like the center of the surface being controlled.
This is not a consideration with pushrods but MUST be compensated for if
using an offset hinge line. Consider the example below: <BR><IMG height=424
hspace=50 src="ackerman_files/Acker-6.jpg"
width=660> </FONT>
<P><FONT face="Times New Roman" size=3> This is exactly
the same as the example above it but the hinge line is now on the top. The
cable connection point must be placed so that the hinge line is the
geometric center instead of the surface. Notice that the circle is centered
at the hinge point and that the red arrows still indicate that each cable is
the same distance from the hinge line. This causes the geometry of the cable
system to go right out the window; each cable will not be straight but
actually at an angle. More importantly, they will be at different angles.
This is a prime example of using Ackerman- this system would be virtually
impossible to compensate for if constant tension was the goal but using a
bit of Ackerman will fix it up perfectly. The cables will now gain slack at
slightly different rates but we don't care about this. A constant tension
system would almost certainly result in a tight point somewhere other than
the neutral (center) point.</FONT>
<P><FONT face="Times New Roman" size=3> I firmly believe
that many people actually introduce Ackerman into both pull-pull and pushrod
control systems without ever knowing that they have done it. Usually, the
control horn is mounted behind the hinge line because of the bevel on the
surface itself. In fact, this is how I found out I was using it..... I
installed (2) pull-pull systems with great results (and Ackerman, although
unwittingly) and then a third but that system became tighter as it was
deflected (the dreaded anti- Ackerman :-) ). After sitting down and thinking
about this for a while, blinding comprehension took hold. As a kid, I had
read about Ackerman and his geometry; a gust of clear thinking made me
realize that I was using it on my model, although by mistake and in one
case, incorrectly. </FONT>
<P><FONT face="Times New Roman" size=3> A few points on
using Ackerman. It is not really desirable, but it is a wonderful tool for
making absolutely sure that the tightest point in the entire servo (and
controlled surface) travel is the neutral point. Slack in the system is not
the goal; having the system NOT tighten as it moves away from neutral is. So
how much Ackerman do we use, how do we measure it and is it critical? Not
much, we don't, and no, it's not. I do not measure any angle or
differential when I use a pull-pull system but rather 'cheat' by simply
offsetting the control horns a small amount. In other words, when I install
the horns, I simply line up the leading edge of the control horn with the
hinge line and then move it back (aft) a slight amount, perhaps 1/16" to
3/32". I do not measure it but know that there is some Ackerman installed,
and <some> is enough. This 1/16" or 3/32" (that's about 1.5 or about 2
mm for you metric types) is the measurement from the hinge line to the
clevis holes on the horn; no other measurement matters.</FONT>
<P><FONT face="Times New Roman" size=3> There could
certainly be too much Ackerman introduced during construction but this isn't
likely. If the cables were attached in such a manner as to create a 30 or
even 45 degree angle, then the slack introduced during deflection would be
far too much, far too soon. That said, look at drawing #4 again and see how
likely it is that this would happen- not very likely. With 3/32 inch of
offset behind the hinge line, the cables will remain tight through
approximately 10 degrees of deflection. After that, there is sufficient
force on the deflected control surface, even at zero forward speed, due to
prop wash. In fact, I do this all the time in the hover; the plane is not
moving but the controls are all deflected a small amount.... no flutter
because even if Ackerman causes a loss of tension in one cable, the prop
wash will provide more than adequate force to hold the pulling cable
taut.</FONT>
<P><FONT face="Times New Roman" size=3> There are
apparently some that have the view that Ackerman, and the resulting slack in
the non-pulling cable, will allow all manner of disastrous things to happen,
starting with the destruction of the flight surface so controlled, and
apparently ending with the death of all living things on planet Earth
:-) Well folks, it just ain't so. It isn't necessary to understand the
mathematical relationship to see that this will work quite well. One easy
test is to put your hand out a car window while driving down the road- start
off with it flat and horizontal, then rotate it a few degrees so that the
wind is trying to lift it. Now drive with your hand in that position until
the wind pushes it down or doesn't push it at all..... it won't happen.
Compare this to a deflected surface- there will be no condition that would
push a deflected surface the <wrong> way, or vary enough in pressure
to cause flutter or any other undesirable condition. The important thing to
remember is that once a surface is deflected even a small amount, one cable
(the 'pulling' cable) is doing all the work while the other is nothing more
than 'along for the ride' at that particular time.</FONT>
<P><FONT face="Times New Roman" size=3> Pull-pull controls
are the best thing to hit model planes since sliced bread (which didn't hit
model planes but was quite a step forward in it's own right :-) ).
They work superbly and have no downside. Ackerman provides the icing on the
cake so that pull-pulls become very easy to install and use. Ackerman also
is a thing of beauty without downside provided it's used in a reasonable
amount but even this is almost assured given normal construction.
</FONT> </P></BLOCKQUOTE></BLOCKQUOTE><!--mstheme--></FONT></BODY></HTML>