Although cars are generally slower and heavier with higher fuel, do they have more grip and downforce as a result of the weight? i.e. are lower fuel cars more prone to understeer and other phenomena associated with low df?
#Fuel level impact on downforce + grip
proud aspen
main fiber
In theory yes, they have more "downforce" and more grip on heavy fuel loads. However, this downforce isn't aerodynamic downforce all things being equal (mass of the fuel may alter the angle of attack of the aero elements which may affect downforce generation), it's the force resulting from the mass of the fuel being accelerated down by the force of gravity. This increased force increases the force going through the tyres which means there is more grip for braking and turning. This doesn't mean this increased grip makes the cars faster though; the cars are overall slower on high fuel loads because of the car having more inertia to overcome to change the velocity and direction of the car.
To get more in depth: this increased inertia manifests as increased centrifugal force, which is the perceived force that throws the car to the outside of the turn while cornering, and is counteracted by the centripetal force of the friction of the tyres (ie. tyre grip), which pulls the car to the inside of the turn. To make a corner a car must have greater centripetal force (Fs) than centrifugal force (F), i.e. if the car goes too fast for the grip provided by the tyres it doesn't make the corner or F>Fs.
The force experienced while turning can be written as F=(mv²)/r, where F is the force, m is the mass of an object, v is the tangential velocity (how fast the object is going i.e. what you would read on the speedometer), and r is the radius of the turn. Assume the grip of the tyres (Fs) is constant (so all same compound, new tyres for quali and new tyres on lap 1 in the race). You would need to make these calculations for each turn, but for the purposes of this example r cannot change, since the turns don't change on a racetrack across a race weekend; therefore the racing line around a track doesn't change. This then means that there are effectively two variables in play: mass and velocity. If mass increases this means F must increase. Also, if velocity increases F must increase.
To reiterate: F must not be greater than Fs if a car is to make a corner. Fs is the same across both examples. On heavy fuel, mass is increased: to satisfy the constraint velocity must decrease accordingly, therefore the car is slower through a turn. On light fuel, mass has been decreased which in turn decreases the centrifugal force: since F has been decreased through decreased mass you can then increase your velocity up to the point where F=Fs, meaning you are at the limit of tyre grip.
https://twitter.com/FiratKeskinF1/status/1485559474928734215
This tweet chain should hopefully help you visualise the problem. It's in Turkish (I think) but the translation of this tweet is:
Forces acting on the vehicle:
🏁 F: Centrifugal force (Blue Arrow)
Centrifugal force: The (virtual) force that sweeps the car out of the corner during rotational motion.
🏁 Fs: Friction force (Red Arrow)
Frictional force:
The force created by friction between the tires and the ground.
main fiber
Now, as for how low fuel manifests in handling characteristics: it depends on the car in question and how it is set up. However, usually high fuel results in understeer, since the weight of the fuel in an F1 car will tend to shift the balance of the car towards the rear axle, which means there should be more force on the rears than the fronts resulting in understeer due to rear grip exceeding front grip. Also, that increased mass usually means you can't carry as much speed through a corner (see above), which will probably also manifest as understeer.
With low fuel the cars are a lot more agile, both due to decreased mass meaning lower force required to turn in general, as well as more velocity through the turn meaning more downforce meaning more grip. Downforce is proportional to velocity squared and to use terminology from above: it effectively increases Fs. This in turn further increases the speed the car can take through a turn since F can increase to match the increase in Fs. Depending on where the downforce is generated this may mean the car understeers (too much rear grip, or the fronts sliding first due to breaking traction) or oversteers (too much front grip, or the rears sliding first due to breaking traction), or neither if you've set the aero balance of the car up well
If you want to have a play around with the concept here's a calculator to hopefully give a more intuitive understanding https://www.omnicalculator.com/physics/centrifugal-force
Just set the Force (F), and radius (r) to a constant number then play with the mass (m). A current F1 car weighs about 800kg on a quali lap (driver and car 798kg, fuel ~2kg give or take a kg) and about 900kg at the start of the race (car plus ~100kg fuel, fuel load varies from track to track though). You'll see that as the mass (m) from the fuel load increases the centrifugal acceleration (g) and tangential velocity (v) decrease, which means a slower speed through the corner