A MATHEMATICAL ANALYSIS OF HYDROPLANING PHENOMENA

A MATHEMATICAL ANALYSIS IS DEVELOPED FOR PREDICTING PHENOMENA ENCOUNTERED WHEN A TIRE ROLLS OR SKIDS ON A PAVEMENT COVERED WITH A WATER FILM. PARTIAL HYDROPLANING IS CONSIDERED WHERE PART OF THE NORMAL FORCE ON THE TIRE IS CARRIED BY DRY CONTACT BETWEEN THE TIRE AND THE PAVEMENT AND ALSO THE ONSET OF TOTAL HYDROPLANING WHERE THE TIRE FIRST BECOMES ENTIRELY SUPPORTED BY HYDRODYNAMIC PRESSURES. THE FLOW IS DIVIDED INTO A FOOTPRINT REGION, AN INLET REGION FORWARD OF THE FOOTPRINT REGION WHERE THE GAP BETWEEN THE TIRE AND THE PAVEMENT IS COMPARATIVELY LARGE, AND AN EXTERIOR FLOW REGION. A PERTURBATION ANALYSIS IS USED ASSUMING THE FLOW IS PRIMARILY VISCOUS IN THE FOOTPRINT REGION AND PRIMARILY INVISCID IN THE INLET REGION. PRESSURES IN THE EXTERIOR FLOW REGION ARE TAKEN EQUAL TO ATMOSPHERIC PRESSURE. THE SOLUTIONS FOR THE SEPARATE REGIONS ARE MATCHED TOGETHER AT THEIR BOUNDARIES. IN PARTIAL HYDROPLANING, A THICK FLUID FILM PENETRATES BETWEEN THE TIRE AND PAVEMENT OVER A PORTION OF THE FOOTPRINT WHILE SEMIDRY CONTACT IS ASSUMED TO EXIST IN THE REMAINDER OF THE FOOTPRINT. THE FLOW THROUGH THE SEMIDRY PORTION OF THE FOOTPRINT IS ANALYZED USING EFFECTIVE FILM THICKNESSES BASED UPON PAVEMENT DRAINAGE CHARACTERISTICS. AN APPROACH FOR DETERMINING THE TIRE DEFORMATION IN THE THICK-FILM PORTION OF THE FOOTPRINT AND THE BOUNDARIES BETWEEN THE THICK-FILM AND SEMIDRY REGIONS IS TAKEN UP. RESULTS OF COMPUTATIONS ARE PRESENTED FOR THE HYDRODYNAMIC PRESSURES AND FLOW FIELDS IN TOTAL HYDROPLANING WHICH WERE OBTAINED ASSUMING THE TIRE SURFACE TO BE PLANE IN THE FOOTPRINT REGION. FOR THE CASE OF PARTIAL HYDROPLANING, THE COMPUTER VARIATIONS IN THE THICK-FILM PENETRATION DISTANCE AND TOTAL FRICTION COEFFICIENT WITH FORWARD SPEED ARE GIVEN FOR A REALISTIC TIRE SURFACE DEFORMATION SUCH THAT A THICK-FLUID FILM EXISTS IN THE CENTRAL PORTION OF THE FOOTPRINT. THE SOURCE OF FRICTION IN THE SEMIDRY REGION OF THE FOOTPRINT IS STUDIED BY ANALYZING THE HYDRODYNAMIC PRESSURES GENERATED WHEN A RUBBER SURFACE SLIDES OVER SIMPLIFIED ASPERITY CONFIGURATIONS. THIS INDICATES THAT DRY CONTACT BETWEEN AN ASPERITY TIP AND THE TIRE SURFACE CAN BE OBTAINED IF THERE IS A SHARP EDGE WHERE THE RUBBER FIRST STARTS TO SLIDE OVER THE ASPERITY AND PROVIDED THERE IS AN ACUTE ANGLE BETWEEN THE SIDE AND TOP FACES OF THE ASPERITY WHOSE INTERSECTION FORMS THIS EDGE. UNDER THESE CONDITIONS, THE EXTREMELY HIGH HYDRODYNAMIC PRESSURES WHICH CAN DEVELOP AT THE VERTEX OF A CONVERGING FLUID WEDGE ARE AVOIDED. COMPUTATIONS OF FRICTION COEFFICIENTS FOR THE SEMIDRY REGION WERE NOT UNDERTAKEN WHICH WOULD INVOLVE A STATISTICAL STUDY OF THE FORMS OF PAVEMENT ASPERITIES. IN THE ANALYTICAL MODEL, LOCAL EMPIRICAL FRICTION COEFFICIENTS ARE USED FOR THE SEMIDRY REGION IN FINDING THE TOTAL FRICTION FORCE ON THE TIRE. /AUTHOR/

• Supplemental Notes:
  • Contract Fh-11-6659, CAL REPORT NO AG-2495-S-1, ADM.,
• Corporate Authors:

  Cornell Aeronautical Laboratory, Incorporated

  4455 Genesee Street
  Buffalo, NY  United States  14221

  Bureau of Public Roads /US

  400 7th Street, SW
  Washington, DC  United States  20590
• Authors:
  • Daughaday, H
  • Tung, C
• Publication Date: 1969-1

Subject/Index Terms

• TRT Terms: Coefficient of friction; Films (Coatings); Hydrodynamics; Hydroplaning; Mathematical analysis; Pavements; Perturbation theory; Pressure; Rubber; Surface drainage; Thickness; Tires; Viscous flow; Water
• Uncontrolled Terms: Film thickness
• Old TRIS Terms: Highway drainage; Highway pavement; Water film
• Subject Areas: Highways; Hydraulics and Hydrology; Pavements; Safety and Human Factors; Vehicles and Equipment;

Filing Info

• Accession Number: 00222576
• Record Type: Publication
• Source Agency: Bureau of Public Roads /US
• Files: TRIS
• Created Date: May 19 1994 12:00AM