2. Next Part of Step II Determining Peak Speed ©Dr. B. C. Paul 2000 revised 2008 Note – The methods outlined here are typical of widely known published engineering practices. The slides contain information taken specifically from the Caterpillar Performance Handbook and screen shots taken from the FPC computer program developed by Caterpillar Equipment Company.

3. Identify Peak Vehicle Speeds l Peak Vehicle Speeds are a function of power a gearing and the resistance to vehicle travel l Resistances are Grade resistance - overcoming (or benefiting from gravity) Rolling Resistance - from flexure of tires and road Wind Resistance

4. Review of Resistance l Wind Resistance not normally an issue for haul trucks - common practice to ignore l Grade Resistance Good old physics problem where break forces into components 2000 * sin (pheta)

5. Simplifying Grade Resistance l Tan (θ) = Rise / Run l At Slopes less than about 20% Tan (θ) = Sin(θ) l Adjusting for Percentage Grade instead of rise over run 20 lbs/ton * % Grade = Grade Res. l We just took the Trig out of Grade Resistance Calculations

6. Rolling Resistance l Tires Sink into Ground - softer ground sink more l Tires Flatten l Driving uphill out of a rut on a flat tire spot l Need to Know Underfoot conditions and Type of Tire (Radial or Bias Ply)

7. Data Comes From an All Knowing Table

8. Reading the Table l Note that Table Gives either lbs/ton or % Grade l One way to treat rolling resistance is as a equivalent grade Puts in the same units as grade resistance so they are additive

9. Two Ways of Totaling Resistance l Equivalent Grade Method Take Grade in % Add Equivalent Grade for Rolling Resistance l Lbs Resistance method Tons Weight * 20 * % Grade Plus Tons Weight * lbs/ton rolling l Note That with Down Hill both can be negative

10. Converting Between l To Convert Total Resistance in% Grade to lbs Weight in tons * 20 * % eqiuv Grade - lbs Resistance l To Convert Total lbs Resistance to % Grade lbs / 20 / Weight in tons = % Grade l I’ll leave you in suspense wondering why we care

11. Getting Rolling Resistance for our FPC Example l FPC Uses the % Grade System Assume I have a firm smooth Road with tires not sinking in About 2.5% for bias ply tires

12. Entering into FPC I had my grade Resistance from my Haulage profile Description. I added my rolling Resistance of 2.5%

13. Peak Speed the Manual Way l Cat 773B 58 ton Mechanical Hauling Dolomite 77 foot Turning Radius so it can make the 85 foot switch back 44.6 yards heaped capacity * 2600 lbs/yd 3 = 57.8 tons Good match l For the level Run Grade Resistance is 0% For hard pack earth 4.25% Total is 4.25% Grade

14. Expressed as Lbs Resistance l Calculated as Lbs Resistance l 43.5 tons Empty (from Cat Book) l * 20 lbs/ton l * 0% Grade l 0 lbs Grade Resistance l 43.5 tons * 85lbs/ton = 3697.5 lbs l Total 3697.5 lbs Resistance

15. Peak Speed Established by Gradability Chart Read Down the Grade Line To the Intersection With the Weight Line Read Over to Gear Curve Read Down to the Speed Speed is 40 mph in 7th Gear

16. By the Rimpull or Lbs Resistance Method Take Calculated Rimpull Requirements (3698 lbs) and go to Rimpull Scale on Chart Read over to Gear Line Read down to Speed Conclude Peak Speed is 40 mph in 7th Gear

17. Checking Other Peak Speeds l Ramp -10% grade -10% Grade + 4.25% Rolling Resistance Total = - 5.75% l Convert to lbs -5.75% * 20 * 87000/2000 = -5002.4 lbs l Time to Go to the Chart

18. Holly Marshmellowed Jelly Beans! Theres no Scale for a negative Grade!

19. Enter the Retarder Chart (No I didn’t Say Retarded) Read Down the Net Favorable Grade to the Truck Weight Line Read Over to Gear Curve Read Down to the Speed Conclude 40 mph in 7th Gear

20. Things to Note About Chart Reading l Some Charts Allow Either Grade or Rimpull Method Cat Gradability Chart Allows Either l Some Allow Only One of the Two Methods Cat Retarder Chart Allows Only Favorable Grade l Since it Varies by Manufacture, you must know both methods

21. More Notes l For the Grade Method we read down either the empty or full weight line For a volume limited truck the loaded truck may not weigh full gross weight so you can’t use pre- printed line - you must use actual loaded weight Some bed liners alter empty weight

22. Manufactures Also Have Brake Performance Charts Note That the Charts Differ in Braking Distance Looking at the Total Negative Grade Distance in a cycle to determine length - Not just grade for the chosen haul segment

23. How Does FPC do This l All the curves are programmed into FPC for Caterpillar Equipment l You have to input the curves for non-Caterpillar equipment.