# Why Does Braking to a Complete Stop Feel Exponentially Harder Than Slowing Down?

When braking to a full stop, anecdotally, when stopping from a high speed (ex, 40 km/h to 0 km/h); for the first half (40 km/h to 20 km/h) it feels a lot easier to slow down compared to the second half (20 km/h to 0 km/h). In addition, it feels easier to lock the brakes and accidentally skid at lower speeds compared to higher speeds. Any reason why this might happen?

• “Exponentially” harder? Why exponential? Please don't use that word unless you mean specifically that constant decrease in speed makes the breaking difficulty increase by a constant factor. Commented Nov 9, 2022 at 23:36
• physics.stackexchange.com/questions/678080/… and physics.stackexchange.com/questions/167111/… if you have the math [I don't ;) Commented Nov 10, 2022 at 9:26
• Actually when you brake from 40 to 0, going from 40 to 20 sheds 3/4 of the total energy, the remaining 1/4 being in the 20 to 0. Commented Nov 10, 2022 at 12:38
• @L.Dutch - that would go towards explaining why constant pressure equals 'over-braking' at the end. Commented Nov 10, 2022 at 12:54
• Just a thought: do your hands get tired easily? If you feel like you're having to squeeze harder that could be why (towards the end of long rides I do suffer from some hand fatigue, only really noticeable stopping on downhills) Commented Nov 10, 2022 at 13:24

Mostly aerodynamics. When you brake, you stop pedalling. So the air resistance actively contributes a braking force which is proportional to the square of your speed.

The wind at 10 km/h has far less braking effect than at 30 km/h so the braking help is reduced.

Try getting really aero, down on the drops, tight clothes, no bags or packs, and repeat your stopping test compared to sitting up as high and wide as you can be. I bet sitting up stops you quicker for the same finger pressure.

A small part may come from your brake pads which have spent the first part of the braking warming up, so their effectiveness initially rises, then peaks, and starts to drop off as the temperature rises.

If braking for long enough, the brakes overheat and the braking surface ceases functioning. This can be the rim/rotor or the pad itself. This is more of a problem on long technical descents where you're braking a lot. Normal riding on the flat will not overheat your brakes at all.

Some hydraulic brakes will heat the liquid oil under use, which gives an odd feeling of the levers pushing back on your fingers. Somewhat disconcerting if you're unaware, and that may feel like a drop in effectiveness when it isn't.

As for skidding, if you are ballsy enough to lock the brakes at full speed, you will skid. It just takes more finger pressure because the rotor/rim is moving faster, has more inertia and that takes more effort to stop. Don't try this in public or on a road please.

• @kaya3 whoops thank you - you're completely correct. Feel free to edit any question/answer for accuracy like that.
– Criggie
Commented Nov 9, 2022 at 21:16
• Locking the back brake in a straight line isn't too serious, and in fact is a good thing to practice in a safe spot. It's rather disconcerting, and it's better if the first time isn't when you hit a slippery spot in traffic. And some (sintered) pads don't get weaker with heat; combined with cable disc brakes there's no deterioration from being stuck behind cars all the way down a mountain pass Commented Nov 9, 2022 at 21:43
• "exponential to the fourth power" is inaccurate. Exponential means that the independent variable is in the exponent position, not raised to any (constant or parametric) power. Commented Nov 10, 2022 at 14:06
• Also, quadratic means x^2, not x^4. Drag is proportional to velocity squared. Commented Nov 10, 2022 at 14:44
• @Criggie no worries, as both a physicist and a pedant I'm glad to have the opportunity to fend off other annoying people like myself Commented Nov 11, 2022 at 19:13

A little bit more on skidding at slow vs. higher speeds: it takes more energy to stop a wheel spinning at higher speeds due to the higher inertia (momentum) to overcome and completely stop the wheel from turning. At this point, the kinetic friction at the braking surface (rotor/pad or rim/pad) is now static friction and the static friction at the tire contact patch is now kinetic friction.

I found a good discussion of this related to cars at Physics Forum

Another factor that applies more to bicycles and rear wheel skidding is weight shift under braking. Under front braking, there is an increased force downward which translates to a higher force needed to get the front tire to skid (break the static friction to become kinetic friction). This is more apparent on pavement vs. dirt, but still there. This weight shift to the front while decelerating correspondingly lessens the force that the rear tire has at its contact patch with the ground. This lessened force lowers the point where the limit of static friction at the contact patch is broken (skidding begins) and now the lower coefficient of kinetic friction applies.

At higher speeds it would take more braking force to create enough weight shift to overcome the energy stored up in a faster spinning rear wheel to create a rear wheel skid. It can be done. It has happened to me in a road race years ago to avoid a crash - and that is the kind of environment where one pulls the brakes on instinct - with lots of adrenaline added, I might add. In this “panic” situation, I pulled in lots of both front and rear brake. The front bit hard enough that the rear locked up in a skid at 45-55 km/h (we were in the final km). I eventually lessened up the rear brake, which stopped the rear skid.

• The comment halfway down that page is very valid - "If you hold a constant pedal load from a higher speed the wheels will lock as you slow down (or the abs will intervene). To threshold brake you need to reduce pedal effort as you slow down. It takes a surprisingly large pedal force to lock up at high speed. The ultimate aim is to have a constant linear deceleration, limited by the grip available." This applies equally to cars & bikes. So many people are incapable of doing this without thinking, that they always jerk to a halt in the last few feet. Commented Nov 10, 2022 at 9:04
• This isn't for 'panic braking' but just to get a smooth deceleration from high speed without coming to a hard jerky stop right at the end. I have no clue whether it's exponential or linear, but it's a gradual decrease in braking pressure as you slow. Commented Nov 10, 2022 at 9:07