Centrifugal force is a concept that every car owner encounters without even knowing it. When the car enters a turn, the tires experience lateral load, and passengers feel like they are being βpressedβ against the door. But how is this force indicated in technical documentation? Why is it used in some sources? Ftsb, in others - Fcf, and in foreign manuals you can find centrifugal force with symbol Fc?
In this article we will analyze not only the standard designations of centrifugal force in physics and engineering, but also show how it is calculated when designing suspension, tires and braking systems. You will find out what units of measurement used in motorsports to evaluate lateral g-forces (hint: it's not always Newtons!), and why errors in calculations can cause your car to skid or even roll over at high speed.
1. Standard notation for centrifugal force in physics and technology
In classical mechanics, centrifugal force is denoted as inertial force, arising in non-inertial (rotating) reference systems. Its main designations:
- π FCentral Bank - Russian-language notation, the most common in domestic textbooks and GOSTs.
- π Fcf - international designation (from English. centrifugal force), used in foreign technical documentation.
- π§ Fc - a simplified designation often found in repair instructions for suspension and brake systems.
- βοΈ Pts - an outdated designation sometimes found in Soviet literature on vehicle dynamics.
It is important to understand that centrifugal force is fictitious force, which appears only in a rotating reference frame (for example, inside a car on a turn). In inertial systems (observer on the side of the road) acts centripetal force, which keeps the body on a circular path. Its designation is Ftss or Fcp (from English centripetal force).
In automotive engineering, it is the centripetal force that is most often used, since it determines maximum permissible cornering speed without skidding. However, in everyday life and when describing the driverβs sensations, the term βcentrifugal forceβ is used - this is what we βfeelβ when the car is βpushedβ off the trajectory.
2. Calculation formula: how to calculate centrifugal force for a car
The basic formula for calculating centrifugal force (FCentral Bank) is derived from Newton's second law and has the form:
Ftsb = m Γ vΒ² / rWhere:
- m - the mass of the car (or its part, for example, a wheel), kg;
- v β linear speed of movement, m/s;
- r β turning radius, m.
For practical calculations in automotive engineering, speed is usually converted from km/h in m/s (divide by 3.6). For example, at speed 90 km/h and turning radius 50 m for a vehicle weighing 1500 kg centrifugal force will be:
Ftsb = 1500 Γ (90 / 3.6)Β² / 50 β 1500 Γ 625 / 50 = 18,750 N (β1.9 tons of force!)This force is distributed between all four wheels, but unevenly: the outer wheels (in relation to the turn) account for up to 70% load. This is why motorsport uses anti-roll bars and adjust the suspension stiffness asymmetrically.
To quickly estimate centrifugal force during a turn, remember: when you double your speed, the force increases by 4 times! For example, at a speed of 60 km/h it is 4 times less than at 120 km/h at the same radius.
3. Units of measurement: newtons, kilogram-force and G-force
In technical documentation, centrifugal force may be indicated in different units. Let's look at the most common ones:
| Unit of measurement | Designation | Automotive applications | Example |
|---|---|---|---|
| Newton | N (N) | Standard unit in the SI system. Used in calculations of suspension, brakes, tires. | FCentral Bank = 5000 N with a mass of 1000 kg on a bend |
| Kilogram-force | kgf (kgf) | An outdated unit, but still found in manuals for old cars (for example, VAZ classic). | 1 kgf β 9.81 N. FCentral Bank = 510 kgf |
| G-overload | g | Used to evaluate lateral accelerations in motorsports and stability testing. | Cornering 0.8g means centrifugal force is 80% of the car's weight |
| Pound-force | lbf | Applicable to American and British standards (e.g. Ford Mustang or Chevrolet Camaro). | 1 lbf β 4.45 N. FCentral Bank = 1125 lbf |
Surgery is more common in motorsports G-overloads, since they are directly related to the pilotβs feelings. For example, in circuit races like Formula 1 or DTM lateral overloads reach 3β4g, and on rally tracks - up to 2.5g. For comparison: a passenger car at the limit of tire adhesion experiences about 0.8β1.0g.
β οΈ Attention: If exceeded1.2gWhen cornering, most production cars begin to lose traction, even with studded tires. This is due to the limitations of the rubber friction coefficient (usuallyΞΌ β 0.8β1.0for dry asphalt).
4. How centrifugal force affects a car: from tires to suspension
Centrifugal force affects all elements of the car, but is especially critical for:
- π Pendants: Increases stress on external shock absorbers and springs, which may result in body roll and loss of control.
- π Shin: shifts the contact patch, reducing traction ("slip" effect). At high speeds this causes
aquaplaningeven on dry roads. - π© Brake system: When turning + braking, the force is distributed unevenly, which may cause locking the inner wheels.
- βοΈ Weight distribution: loads the outer wheels, unloading the inner ones (risk of loss of traction).
Manufacturers combat these effects by:
- π Anti-roll bars (reduce roll).
- π οΈ Adaptive suspension (for example, Magnetorheological Suspension in Audi or BMW).
- π Stability control systems (
ESC,DSC), which brake individual wheels. - ποΈ Tires with asymmetric tread pattern (for example, Michelin Pilot Sport 4S).
Why is centrifugal force more dangerous on trucks?
Trucks have a high center of gravity and heavy weight, which increases the risk of rollover. For example, at a speed of 60 km/h and a turning radius of 30 m, the centrifugal force for a truck weighing 20 tons reaches β120,000 N (12 tons!). This can shift the load or even tip the vehicle if the center of gravity is higher than 1.5 m from the road.
5. Practical examples: calculation for real cars
Let's consider how centrifugal force manifests itself in situations:
Example 1: Passenger car on a roundabout
Conditions:
- Car: Toyota Corolla, mass
1300 kg. - Speed:
80 km/h. - Turning Radius:
40 m(typical ending).
Calculation:
Ftsb = 1300 Γ (80 / 3.6)Β² / 40 β 1300 Γ 494 / 40 β 16,000 N (β1.6 tons)This force is distributed between the wheels and tries to βmoveβ the car off the trajectory. If the tire adhesion coefficient ΞΌ = 0.8, the maximum permissible adhesion force will be 1300 Γ 9.81 Γ 0.8 β 10,200 N. Thus, the car is already at the limit of traction and may start to slide!
Example 2: Sports car on a race track
Conditions:
- Car: Porsche 911 GT3, mass
1430 kg. - Speed:
150 km/h. - Turning Radius:
100 m(flat turn).
Calculation:
Ftsb = 1430 Γ (150 / 3.6)Β² / 100 β 1430 Γ 1736 / 100 β 24,800 N (β2.5 tons)Thanks to wide tires and low center of gravity Porsche can withstand lateral overloads up to 1.3g, so this turn will take place without skidding. However, for a production sedan this would be critical.
Assess turning radius and speed|Make sure shock absorbers are in good condition|Check tire pressure (especially external tires)|Reduce speed in advance, without sudden braking on the curve-->
6. Errors in calculations: what are the consequences of incorrectly taking into account centrifugal force
Ignoring centrifugal force when designing or repairing a car can lead to serious consequences:
- π¨ Skidding on a turn: If the suspension is not designed to handle lateral loads, the car will lose control. Typical for tuned cars with stiff springs.
- π₯ Rollover: relevant for tall cars (SUVs, minibuses). For example, Mercedes-Benz Vito at a speed of 70 km/h on a turn with a radius of 25 m it can tip over.
- π₯ Tire overheating: Uneven distribution of force leads to localized tread wear and the risk of tire explosion.
- βοΈ Stabilizer failure: if the designed load is exceeded, the anti-roll bar may become deformed (a common problem with Renault Megane II).
Case study: in 2018 on the track NΓΌrburgring test BMW M5 (F90) lost control at a speed of 240 km/h due to an error in setting up the electronic stabilization systems. The centrifugal force on that turn exceeded 35,000 N, which led to a skid and accident. After the incident, the manufacturer updated the firmware ESC for all cars in the series.
β οΈ Attention: When replacing wheels with wider or lower profile ones necessarily recalculate the permissible lateral loads! Tires with speed index T (190 km/h) may not withstand centrifugal force at a speed of 220 km/h, even if the car is technically capable of developing it.
7. How to reduce the influence of centrifugal force: tips for drivers
Even if you are not an engineer, a few simple rules will help reduce risks:
- π Reduce speed before entering the turn: Braking on a curve increases centrifugal force and the risk of skidding.
- π Use the "smooth steering" technique: Sharp steering at high speed increases roll.
- π Check your tire pressure: Reduced pressure reduces the contact patch and grip.
- βοΈ Distribute the load evenly: Heavy objects in the trunk increase the center of gravity.
- π οΈ Keep an eye on the suspension: Worn shock absorbers increase roll by 30β40%.
To illustrate, if you are entering a roundabout at a speed 90 km/h instead of recommended 60 km/h, the centrifugal force will increase by 2.25 times (since it depends on the square of the speed). This means that your car will need traction like a race car!
The most effective way to reduce centrifugal force is increase turning radius. For example, at a roundabout, it is better to take the outer path, even if it increases the distance.
FAQ: Frequently asked questions about centrifugal force in cars
Why is centrifugal force felt stronger on motorcycles than in a car?
On motorcycles, the center of gravity is much higher, and the mass is concentrated on two wheels. When turning, the rider must lean with the motorcycle to compensate for centrifugal force. For example, at a speed of 100 km/h and a radius of 20 m, the force reaches β2000 N for a motorcycle weighing 250 kg, which requires tilting 40β45Β°.
How does centrifugal force affect tire wear?
With constant turns (for example, on serpentine roads), the outer wheels experience increased load, which leads to uneven tread wear. On front wheel drive vehicles, front tire wear may vary by 20β30% from the rear. Solution: regular rearranging wheels (every 10,000 km).
Is it possible to completely eliminate centrifugal force?
No, but its influence can be minimized. In motorsport they use:
- π Aerodynamic elements (wings) that create downforce.
- π§ Active suspension, which changes the hardness in real time.
- π High grip tires (for example, Pirelli P Zero Trofeo R).
In production vehicles, full compensation is not possible, but systems like ESC or Torque Vectoring (for example, in Honda Civic Type R) reduce risks.
How is centrifugal force related to hydroplaning?
Centrifugal force displaces the tire's contact patch, reducing the area that can drain water. For example, at a speed of 100 km/h and a radius of 50 m on a wet road, a layer of water is sufficient 3β4 mmto lose traction. This is due to the fact that the outer part of the tire (loaded with force) does not have time to βcut throughβ the water layer.
Why do they talk about "lateral Gs" in motorsports and not Newtons?
G-overload more convenient for assessing the impact on the pilot and the car, since they show how many times the force exceeds the weight of the car. For example, 1.5g means that the centrifugal force is 50% greater than the weight of the car. B Formula 1 pilots test up to 5g in turns, which requires special physical training.