question: How does a tire stay seated on a wheel even if all the pressure has been lost?
comment: The reason that you need force to remove it is because you need force to get it there in the first place. The inner diameter of the tire is lower the the outer diameter of the wheel so need to stretch/deform it to get it to fit and for large tires you need a lot of force to get it there. The edge of the tire is the tire bead and it is in most case high tensile strength steel wire encased in rubber so it is inflexible and strong so it will stay on the wheel regardless of the pressure and is har to remove. If you ever tried to change tie you notice that even remove a bicycle tire can be hand and they the are design so you can do it by hand with small tool but larger tier are designed for machines assistance when you out them on and remove them.
passages: For example, a study at the University of Oldenburg found that Schwalbe Standard GW HS 159 tires, all with a width of 47 mm and an inflation pressure of , but made for various diameter rims, had the following rolling resistances:
  
  The author of the cited paper concludes, based on the data presented therein, that Crr is inversely proportional to inflation pressure and to wheel diameter.
  
  Section::::Parameters.:Forces and moments generated.:Cornering force and camber thrust.
   Section::::Performance characteristics.
  
  The interactions of a tire with the pavement are a complex. Many of the details are modeled in Pacejka's Magic Formula. Some are explained below, alphabetically, by section.
  
  Section::::Performance characteristics.:Dynamics.
   Stress in the "poloidal" direction ("hoop" or "circumferential" stress if the tire is considered a long cylinder) is more complicated, varying around the minor circumference and depending on the ratio between the major and minor radii, but if the major radius is much larger than the minor radius, as on most bicycle tires where the major radius is measure in hundreds of mm and the minor radius is measured in tens of mm, then stress in the Poloidal direction is close to the hoop stress of cylindrical thin-walled pressure vessels:
   One published guideline for clincher inflation pressure is to pick the value for each wheel that produces a 15% reduction in the distance between the wheel rim and the ground when loaded (i.e. with the rider and cargo) compared to when unloaded. Pressures below this led to increased rolling resistance and likelihood of pinch-flats. Pressures above this led to less rolling resistance in the tire itself, but to larger energy losses in the frame and rider.
   These requirements can be met by systems with external pressure sensors that connect to the valve stem on each tire. When tires are replaced, the sensor is moved to the new tire.
   "Rolling resistance increases in near proportion as wheel diameter is decreased for a given constant inflation pressure."
  
  Section::::Technical aspects.:Rotating mass.
   Three main techniques for attaching a bicycle tire to a rim have been developed: clincher, wired and tubular. Clinchers originally did not have wire in the beads and the shape of the bead interlocked with a flange on the rim, relying on air pressure to hold the tire bead in place. However, this type of tire is no longer in general use and the term "clincher" has transferred to the modern wired-on tire. For the remainder of this article, the modern use of the word "clincher" will be assumed.
   Tire balance
  
  Tire balance, also called tire unbalance or tire imbalance, describes the distribution of mass within an automobile tire or the entire wheel (including the rim) on which it is mounted.
   Section::::Dynamic balance.
   Section::::Parameters.:Inflation pressure.:Effect on carcass stress.
  
  Bicycle tires are essentially toroidal thin-walled pressure vessels and if the carcass is treated as a homogeneous and isotropic material then stress in the "toroidal" direction ("longitudinal" or "axial" stress if the tire is considered a long cylinder) can be calculated as:
  
  where:
  
  BULLET::::- "p" is internal gauge pressure
  
  BULLET::::- "r" is the inner, minor radius of the carcass
  
  BULLET::::- "t" is thickness of the carcass
   Section::::Primary cause.
  
  The primary cause of pneumatic tire rolling resistance is hysteresis:
  
  A characteristic of a deformable material such that the energy of deformation is greater than the energy of recovery. The rubber compound in a tire exhibits hysteresis. As the tire rotates under the weight of the vehicle, it experiences repeated cycles of deformation and recovery, and it dissipates the hysteresis energy loss as heat. Hysteresis is the main cause of energy loss associated with rolling resistance and is attributed to the viscoelastic characteristics of the rubber.
   Section::::Parameters.:Inflation pressure.:Effect of atmospheric pressure.
   Additional energy is lost from the wheel-to-road interface. This is termed rolling resistance which is predominantly a deformation loss. This energy is also lowered by the use of a wheel (in comparison to dragging) because the net force on the contact point between the road and the wheel is almost perpendicular to the ground, and hence, generates an almost zero net work. This depends on the nature of the ground, of the material of the wheel, its inflation in the case of a tire, the net torque exerted by the eventual engine, and many other factors.
   Due to the fact that the wheel and tire's motion is constrained by the suspension links on the vehicle, the motion of the wheel package in the front view will scribe an imaginary arc in space with an "instantaneous center" of rotation at any given point along its path. The instant center for any wheel package can be found by following imaginary lines drawn through the suspension links to their intersection point.
   Also, because real tires have a finite contact patch with the road surface that can generate a scrub torque, and when in a turn, can experience some side slipping as they roll, they can generate torques about an axis normal to the plane of the contact patch.
   The most basic maintenance item is keeping the tires correctly inflated; this can make a noticeable difference as to how the bike feels to ride. Bicycle tires usually have a marking on the side wall indicating the pressure appropriate for that tire. Note that bicycles use much higher pressures than cars: car tires are normally in the range 30 to 40 pounds per square inch while bicycle tires are normally in the range 60 to 100 pounds per square inch.
   In the first situation, the car is moving and the pressure of one of the tires moves from 45 psi to 41 psi over 15 minutes. As the pressure in the tire is decreasing, a series of events containing the tire pressure is generated. In addition, a series of events containing the speed of the car is generated. The car's Event Processor may detect a situation whereby a loss of tire pressure over a relatively long period of time results in the creation of the "lossOfTirePressure" event. This new event may trigger a reaction process to note the pressure loss into the car's maintenance log, and alert the driver via the car's portal that the tire pressure has reduced.
   Bicycle tires generate forces and moments between the wheel rim and the pavement that can affect bicycle performance, stability, and handling.
  
  Section::::Parameters.:Forces and moments generated.:Vertical force.
  
  The vertical force generated by a bicycle tire is approximately equal to the product of inflation pressure and contact patch area. In reality, it is usually slightly more than this because of the small but finite rigidity of the sidewalls.
  
  The vertical stiffness, or spring rate, of a bicycle tire, as with motorcycle and automobile tires, increases with inflation pressure.
  
  Section::::Parameters.:Forces and moments generated.:Rolling resistance.
   Inflation is key to proper wear and rolling resistance of pneumatic tires. Many vehicles have monitoring systems to assure proper inflation. 
   Also worth mentioning is the fact that tires simply lose air over time. A brand new tire, properly inflated, will lose air even with no punctures present. This is mainly due to the design of the valve stem, among other reasons. Given enough time, a tire can fully deflate with no outside intervention.
  
  Section::::Flat tire repair.:Bicycles.
   The final method, the tire plug, can be performed without removing the tire. The penetrating object is removed from the tire, and a plug coated in rubber cement then inserted with a handle, typically supplied with the kit. Many technicians consider plugs less reliable than patching though more reliable than sealant. 
   Forces occurring between the motorcycle and the road (such as those that result in accelerating, decelerating and turning) occur at the contact patch through friction and normal forces. There is a limited amount of force tangential to the road that the contact patch can transmit before the tire begins to lose traction, and therefore slide or skid.
   Some railway wheels and other older types of rolling stock are fitted with railway tires in order to prevent the need to replace the entirety of a wheel. The tire, usually made of steel, surrounds the wheel and is primarily held in place by interference fit.
   Tires have a large influence over bike handling, especially on motorcycles, but also on bicycles. Tires influence bike dynamics in two distinct ways: finite crown radius and force generation. Increase the crown radius of the front tire has been shown to decrease the size or eliminate self stability. Increasing the crown radius of the rear tire has the opposite effect, but to a lesser degree.
   These two properties are not linearly proportional to the area of the contact. For example, a 10% change in load or inflation pressure usually does not result in a 10% change in the contact patch area because the load or pressure on a tire can be altered freely, and the contact patch area is affected by the tire geometry and stiffness. Further, the size of the contact patch cannot be simply calculated as load divided by inflation pressure, and the average contact pressure a tire has with the road surface is not equal to the inflation pressure. 
  