[python] Re: Lean disturbances (and Dirk's code)

  • From: mtb@xxxxxxx
  • To: python@xxxxxxxxxxxxx
  • Date: Mon, 28 Feb 2005 22:07:38 -0800

At 08:25 PM 2/28/2005 +0100, you wrote:

what could these numbers tell us? 

Well, I just tried:
pivotTorque = frontMass2PivotAxis*math.sin(turnAngle)* \
           math.sin(pivotAngle)*frontMass  #kg-force cm

pivotZforce = frontMass2PivotAxis/d4*math.sin(turnAngle)* \
                    math.sin(pivotAngle)*frontMass
print "rearMassAtPivot: %.1f, pivotZforce: %.1f" %
        (rearMassAtPivot, pivotZforce)

for:
    trlP2Rear = 110.
    trlP2Front = -10.     ## trail
    pivotAngle = 35.  * math.pi / 180.0 # deg from vertical
    turnAngle = 45.  * math.pi / 180.0
    rearMass = 70.
    rearMassZ = 30.
    rearMassX = 100.
    frontMass = 15.
    frontMassZ = 40.
    frontMass2PivotAxis = 20.

riseAngle: 0.667972deg,   rearmass rise: 1.163767cm
frontMassFall: 6.548251cm
rearMassAtPivot: 63.6, pivotZforce: 14.9

If I'm correct, (probably not too far off) then it seems that the lift caused by the weight of the front about the pivot (14.9) offsets about 1/4 of the force of the body weight at the pivot. The farther out front the mass is and the shorter the trail, the stronger the offset.
Code attached.

Dirk once said that there exists a specific angle for
every frame geometry where the pivot rise is maximal.
Which data does one need to calculate this angle and
how is it done?


I added a nested loop with angle and trail. My code gives this:
pivot    trail->
angle   10      5       0       -5      -10     -15     -20     -25
30      -0.26   -0.124  0.0     0.114   0.218   0.315   0.404   0.487
31      -0.265  -0.127  0.0     0.116   0.223   0.321   0.412   0.497
32      -0.27   -0.129  0.0     0.118   0.227   0.327   0.419   0.506
33      -0.274  -0.131  0.0     0.12    0.23    0.332   0.426   0.514
34      -0.279  -0.133  0.0     0.122   0.234   0.337   0.433   0.521
35      -0.282  -0.135  0.0     0.123   0.237   0.342   0.438   0.528
36      -0.286  -0.136  0.0     0.125   0.24    0.346   0.444   0.535
37      -0.289  -0.138  0.0     0.126   0.242   0.349   0.448   0.54
38      -0.292  -0.139  0.0     0.127   0.244   0.352   0.452   0.545
39      -0.294  -0.14   0.0     0.128   0.246   0.355   0.456   0.549
40      -0.296  -0.141  0.0     0.129   0.248   0.358   0.459   0.553
41      -0.298  -0.142  0.0     0.13    0.249   0.36    0.462   0.556
42      -0.299  -0.143  0.0     0.131   0.251   0.361   0.463   0.558
43      -0.3    -0.143  0.0     0.131   0.251   0.362   0.465   0.56
44      -0.301  -0.143  0.0     0.131   0.252   0.363   0.466   0.561
45      -0.301  -0.143  0.0     0.131   0.252   0.363   0.466   0.561
46      -0.301  -0.143  0.0     0.131   0.252   0.363   0.465   0.561
47      -0.3    -0.143  0.0     0.131   0.251   0.362   0.464   0.559
48      -0.299  -0.143  0.0     0.131   0.25    0.361   0.463   0.558
49      -0.298  -0.142  0.0     0.13    0.249   0.359   0.461   0.555
50      -0.296  -0.141  0.0     0.129   0.248   0.357   0.458   0.552
51      -0.294  -0.14   0.0     0.128   0.246   0.355   0.455   0.548
52      -0.292  -0.139  0.0     0.127   0.244   0.352   0.451   0.544
53      -0.289  -0.138  0.0     0.126   0.242   0.349   0.447   0.539
54      -0.286  -0.136  0.0     0.125   0.239   0.345   0.442   0.533
55      -0.283  -0.135  0.0     0.123   0.236   0.341   0.437   0.526
56      -0.279  -0.133  0.0     0.122   0.233   0.336   0.431   0.519
57      -0.275  -0.131  0.0     0.12    0.23    0.331   0.425   0.511
58      -0.271  -0.129  0.0     0.118   0.226   0.326   0.418   0.503
59      -0.266  -0.127  0.0     0.116   0.222   0.32    0.41    0.494
60      -0.261  -0.124  0.0     0.114   0.218   0.314   0.402   0.485
61      -0.255  -0.122  0.0     0.111   0.213   0.307   0.394   0.474
62      -0.25   -0.119  0.0     0.109   0.208   0.3     0.385   0.464
63      -0.244  -0.116  0.0     0.106   0.203   0.293   0.376   0.452
64      -0.237  -0.113  0.0     0.103   0.198   0.285   0.366   0.441
65      -0.231  -0.11   0.0     0.1     0.193   0.277   0.356   0.428
66      -0.224  -0.107  0.0     0.097   0.187   0.269   0.345   0.415
67      -0.217  -0.103  0.0     0.094   0.181   0.26    0.334   0.402
68      -0.209  -0.1    0.0     0.091   0.175   0.252   0.323   0.388
69      -0.202  -0.096  0.0     0.088   0.168   0.242   0.311   0.374
70      -0.194  -0.092  0.0     0.084   0.162   0.233   0.298   0.359
71      -0.186  -0.088  0.0     0.081   0.155   0.223   0.286   0.344
72      -0.177  -0.084  0.0     0.077   0.148   0.213   0.273   0.328
73      -0.169  -0.08   0.0     0.073   0.141   0.202   0.26    0.312
74      -0.16   -0.076  0.0     0.069   0.133   0.192   0.246   0.296
75      -0.151  -0.072  0.0     0.066   0.126   0.181   0.232   0.279
76      -0.142  -0.067  0.0     0.062   0.118   0.17    0.218   0.262
77      -0.132  -0.063  0.0     0.057   0.11    0.159   0.203   0.245
78      -0.123  -0.058  0.0     0.053   0.102   0.147   0.189   0.227
79      -0.113  -0.054  0.0     0.049   0.094   0.136   0.174   0.209

A maximum at 45deg.

PS: If are working on a config file for your program, could
you please include flags for metric/imperial and maybe the
possibility of changing the limiting values for the sliders.

I'll try to get to it soon. I did upload a new version to :
http://rjs.org/Python/FrameGeometry.zip
More positive trail, and the text output on "Plot" gives appropriate speed. The criteria coefficients are numeric now (it is when they go positive that they indicate stability). It should indicate if the formulas are close to positive, and so might be almost stable.

Hope your weather improves,
Ray

Ours is a bit foggy. Cam on top of the hill behind us ;-)
http://archive.hpwren.ucsd.edu/I700/LaJollaCoast/Data/TODAY/

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