Ackermann

HelpThe simple spreadsheet format of this program imposes some limitations.Some combinations of data will crash the program and, because you can only change one entry at a time,it is likely that unstable situations will occur when you try to make radical changes to the layout.If the geometry is impractical - say the combined lengths of the steering arm and trackrod are too short,(or too long) ever to fit - it will crash.After a crash, you will need to 'Reset' the Visual Basic for Applications (VBA) program that creates the diagram.To do this, Click the Visual Basic Editor icon in the VB toolbar.If it isn't shown, select View|Toolbars then click Visual Basic if it isn't already 'checked'.Find the Visual Basic Editor icon by passing the cursor over the icons until the Tool Tip pops up to identify it.Click on it to show the Editor screen.You will find that the program has stuck on the highlighted line.Click on Run|Reset, then go back to the usual spreadsheet screen by clicking the 'XL' (Excel) icon,usually found on the extreme left of the Toolbar, when the Editor is showing.Another limitation is the inability automatically to update the diagram when new information is entered.Follow the instructions given on the diagram screen to delete old lines.Erase any remaining lines by clicking on them individually and pressing Delete.

DataHalf Axle25inches2522.5Half AxleHalf Rack7714Half RackSteering Arm-3-34Steering ArmTrack Rod2020.57Track RodRack Back-8-85Rack BackWheelbase838386WheelbaseStatic toe-in (per wheel)0degrees000Static toe-in (per wheel)Front tyre slip angle10degrees0.174532925200Front tyre slip angleRear tyre slip angle10degrees0.174532925200Rear tyre slip angleSteer arm angle (static)25.4degreesThese datasets can be copied and pasted to cells B1 to B9,Arm - rod angle (static)79.9degreesto illustrate front and rear-mounted racks.Ackermann effect (static)158per centPositive (pulling on trackrod)Negative (pushing)Rack Travelalpha cos termbeta cos termtan termalpha cos termbeta cos termtan termACOS termATAN termTheta pullTheta pushMeanDiffDiff/meanTurn RadiusLangenspergerbeta acos termbetaArm-rod angleTheta rightRadius ftRadius with slipTurn centre fwdLangensperger slipmean-slipRadiusForward of front axle00.02538365410.1750000-0.44444444440.0253836541-0.444444444488.55-23.9625.4288.55-23.9625.420.00.00.00.00.0Infinite0.0079.956.079.90.0-10.00.020.0315015722-0.44493882090.0192703113-0.443951165488.19-23.9925.7988.90-23.9425.040.40.40.4-0.0-0.112710-0.00-0.41059.201028.442176.1-0.04-9.61234120930.040.0376240752-0.44543429840.0131615343-0.4434589887.84-24.0126.1789.25-23.9224.670.70.70.70.00.26355-0.01-0.7529.57514.781089.2-0.07-9.3617710060.060.0437511728-0.44593088070.0070573133-0.442967884887.49-24.0326.5489.60-23.8924.301.11.11.10.00.34236-0.01-1.1353.01343.55726.9-0.11-8.941236440.080.0498828745-0.44642857140.0009576389-0.442477876187.14-24.0626.9289.95-23.8723.921.51.51.50.00.43177-0.02-1.5264.72257.92545.7-0.14-8.530954630.10.0560191901-0.4469273743-0.0051374984-0.441988950386.79-24.0827.2990.29-23.8423.551.91.91.90.00.52541-0.04-1.9211.74206.53437.0-0.16-8.124783540.20.0867703161-0.4494382022-0.0355454618-0.439560439685.02-24.2029.1892.04-23.7321.693.83.73.70.01.01268-0.15-3.7105.71103.70219.4-0.25-6.312441360.30.1176382505-0.4519774011-0.0658414184-0.437158469983.24-24.3231.0893.78-23.6119.845.75.65.60.11.4843-0.33-5.670.2969.35146.7-0.26-4.4832640.40.1486242242-0.4545454545-0.0960265385-0.434782608781.45-24.4432.9995.51-23.5017.997.67.47.50.11.9630-0.59-7.452.5352.13110.3-0.20-2.5626270.50.1797294797-0.4571428571-0.1261019802-0.432432432479.65-24.5734.9297.24-23.3916.149.59.39.40.22.4502-0.92-9.341.8241.7588.3-0.06-0.650150.60.2109552719-0.4597701149-0.1560688896-0.430107526977.82-24.6936.8798.98-23.2714.2911.511.111.30.32.9416-1.33-11.134.6534.7973.60.151.3417-90.70.2423028674-0.4624277457-0.1859284009-0.427807486675.98-24.8238.84100.72-23.1612.4513.413.013.20.53.4354-1.81-13.029.5029.7963.00.453.2357-200.80.273773545-0.4651162791-0.2156816362-0.425531914974.11-24.9440.83102.46-23.0510.6015.414.815.10.63.9307-2.36-14.825.6026.0155.00.825.1312-280.90.3053685952-0.4678362573-0.2453297059-0.423280423372.22-25.0742.85104.20-22.948.7417.416.717.10.84.4271-2.99-16.722.5423.0548.81.277.1277-3410.3370893204-0.4705882353-0.2748737084-0.421052631670.30-25.2044.90105.95-22.836.8819.518.519.00.95.0241-3.69-18.520.0820.6543.71.819.0248-391.10.3689370347-0.4733727811-0.3043147302-0.418848167568.35-25.3346.98107.72-22.735.0121.620.421.01.25.5216-4.47-20.418.0318.6739.52.4211.0224-431.20.4009130637-0.4761904762-0.3336538462-0.416666666766.36-25.4649.10109.49-22.623.1323.722.323.01.46.1196-5.32-22.316.3117.0036.03.1213.0204-471.30.4330187447-0.4790419162-0.3628921195-0.41450777264.34-25.6051.26111.28-22.511.2425.824.225.01.76.6178-6.25-24.214.8315.5632.93.9015.0187-501.40.4652554263-0.4819277108-0.3920306017-0.41237113462.27-25.7353.46113.08-22.41-0.6728.026.127.12.07.2162-7.24-26.113.5414.3130.34.7617.1172-531.50.4976244684-0.4848484848-0.4210703327-0.410256410360.16-25.8755.71114.90-22.31-2.6030.328.029.22.37.8149-8.31-28.012.4013.2127.95.7119.2159-551.60.5301272417-0.487804878-0.4500123411-0.408163265357.99-26.0058.02116.74-22.20-4.5432.630.031.32.68.4137-9.45-30.011.3912.2225.96.7421.3147-571.70.5627651282-0.490797546-0.4788576439-0.406091370655.75-26.1460.39118.61-22.10-6.5135.031.933.43.09.1126-10.66-31.910.4711.3424.07.8623.4136-591.80.5955395203-0.4938271605-0.5076072469-0.40404040453.45-26.2862.83120.50-22.00-8.5037.433.935.73.59.8116-11.93-33.99.6410.5322.39.0725.7126-611.90.6284518209-0.4968944099-0.5362621446-0.402010050351.06-26.4265.36122.43-21.90-10.5339.935.937.94.010.5106-13.27-35.98.879.7920.710.3527.9117-6220.6615034433-0.5-0.5648233203-0.448.59-26.5767.98124.39-21.80-12.5942.638.040.34.611.398-14.67-38.08.169.1019.211.7330.3109-64

Data

Actual differenceDifference needed for rail-like trackingRack travel (inches)Steer angle difference (degrees)

Diagram

Left wheel angleRight wheel angleDifferenceTurn radius (feet)Forward movement of turn centre (inch)Rack travel (inch)Steer angles / radiusActual wheel angles

Half plan view of steering geometryIf you want to display the turn centres, check the box on the 'Data' sheet.Ackermann158percentScale OKYou have to erase the drawings manuallyClick on the arrow near the 'Draw' in lower left corner.Left click and drag a box to enclose all the lines making up the drawing.Release to close the box. Press 'Del' to erase the lines.Click on the 'Draw' arrow to cancel it.A new drawing will be done when you enter new data into the spreadsheet.This procedure is necessary because Microsoft appears not to include automatic facilities for redrawing in the VBA language built into Excel.Blue crosses show turn centre at indicated rack travel and turn radius

CLhalf axlehalf racksteering armtrack rodrack backSchematic layoutsteer arm anglearm-rod angleMJM:Highlighted boxes are the VARIABLES used in the calculations. Change them to suit your needs.Mike:This is the lateral distance from the chassis centre-line of the steering axis (kingpin) at the height of the steering arm.Mike:This is the lateral distance from the chassis centre-line of the end of the steering rack - where the track-rod is connected to it.Mike:This is the actual length of the track-rod, joint to joint.Mike:This is the actual length of the steering arm from the kingpin to the track-rod-end.Mike:This is the rack's distance behind the'axle' - the line joining the front wheel centres. For forward mounted rack, use a negative length.Mike:Highlighted boxes are the VARIABLES used in the calculations. Change them to suit your needs.Mike:Highlighted boxes are the VARIABLES used in the calculations. Change them to suit your needs.Mike:Highlighted boxes are the VARIABLES used in the calculations. Change them to suit your needs.