Why do modern F1 cars look so slow ? Yann Thorimbert January 2023 Introduction Modern Formula 1 (F1) cars appear slow to the TV spectators. As a show and a business based on the entertainement it provides to the spectators, this apparent slowness of F1 is an issue in many regards. First, young people interested in car com- petitions are most often attracted by their speed and the sense of speed they give, in first instance. To attract new spectators, a car competition should pay attention to the experience of the footage it provides, in particular when competitors propose a better sense of speed on TV ( i.e. NASCAR series, WRC). Second, many of the current F1 fans came to it when cars seemed fast. It would not come as a surprise that they stop following F1 for the opposite reason. All the explanations of the apparent slowness of F1 found on the Web primarily focus on the advancements in image quality, zoom and filming methods in general. Though these considerations intervene for sure in the global explanation, they are mostly details in regard of more important, though subtle reasons. Here is a brief summary of what can be found on the Internet : — From flowracers.com 1 : ≪ F1 cars look slow on TV because of the angles and the distances between the cameras and the cars. Zooming and panning to keep the cars centered on the screen also makes them appear slower than they are. F1 cars also look slower on TV because of advancements in filming and image quality. ≫ This explanation is only half true. A small car filmed the same way a F1 is filmed can appear fast when the F1 doesn’t, as on this video : xxxx — According to motorsport.com 2 , the 4/3 format was responsible for a good sense of speed of F1, as well as the image definition. This hypothesis likely is wrong, as illustrated by this video : xxxx. However, the sound of the new engines and the stability of the new cars is a part of the explanation we agree with, though the reason why the sound impact the sense of speed involve more complex concepts than the engine RPM solely. — The sense of speed on onboard footage use immensely impacted by the field of view of the onboard camera 3 . In this article, we only treat the problem of TV footage from the side of the track, not onboard cameras. 1. https://flowracers.com/blog/why-f1-cars-look-slow-on-tv/ 2. https://www.motorsport.com/f1/news/old-laps-cars-faster-tv/ 3. See https://www.youtube.com/watch?v=e9OriySqLjQ for an impressive illustration. 1 In this article, we give physically sound explanations to the apparent slowness of mordern F1 cars. 1 Size of the car There are two main obstacles to entertainement caused by the increase in car sizes. The first one is obvious and already extensively discussed within the community : overtakings are more difficult when cars are large, especially on narrow tracks like Monaco. The second one is more difficult to grasp, but in my opinion almost as [dommageable] : the sense of speed [ ́ emanant] from the car. 1.1 Self-crossing duration Comparing animations of short and length cars travelling at the same speed, it is clear that the former ones appear faster, as an illusion. Since such an observation cannot be made when no background nor external markers are present around the car, we assume that the explanation of this effect lies in the comparison, by the human eye, between the size of the car and some external markers ( e.g. a tree, some spectators, road details, etc). More precisely, static details are used as markers to approximate the speed of an object. Let denote by ≪ self-crossing duration ≫ the amount of time taken by a car to travel a distance that is equal to its own length. For a car with length L and speed v , the self-crossing duration ∆ t is equal to ∆ t = L v . (1) Therefore, when the size of a car is decreased by a factor two, it appears twice faster in the sense of self-crossing duration. This is why, for instance, the McMurtry Sp ́ eirling seems so fast in the videos of Goodwood hillclimb, despite being less than 1 second faster than the VW I.D. R – a velocity difference the eyes alone cannot detect for two identically looking cars. 1.2 Camera angle change In the previous subsection, we discussed the importance of external details for the human observer to appreciate the speed of an object. However, even in the absence of external details, it is possible to evaluate the speed of an object passing by our eyes. This second way for our brain to approximate the object velocity is related to the rate of change of its apparent size. Consider a car of length L approaching an observer O , as in figure 1. D is the distance from the car to the observer when the car is at the closest point from the observer ( i.e. the distance from the observer to the road). d denotes the distance from the car to the closest point to the observer. The angular size of the car is β . Since tan( α ) = D/d and tan( α + β ) = D/ ( d − L ), we can express the angular size as : β = tan − 1 ( D d − L ) − tan − 1 ( D d ) (2) In equation (2), D is a constant for a given road, but d is a function of the time and the velocity of the car : d = v · t . Hence, the relationship between the angular size of 2 a car, its velocity and the distance between the observer and the road is given by : β ( t ) = tan − 1 ( D v · t − L ) − tan − 1 ( D v · t ) (3) Figure 1 – Parameters used to express the angular size ( β ) of a car passing by an observer O Figure 2 display the value of β as a function of time, for three vehicles of different sizes travelling at 50 km/h. The length of the ferrari F1-75 is 5.5 m, the length of the Ferrari F2004 is 4.5 m and the length of the RC car is 0.5 m. It is clear from the plot that the RC car appears as a ≪ flash ≫ to the observer, in terms of angular size, whereas the F1-75 is much slower to appear and fade out. Figure 2 – Time evolution of the normalized angular size of a car passing by a camera with v = 50 km / h, for 3 differents cars. Illustrer avec petite VS grosse voiture en vrai (goodwood par exemple), puis RC cars ` a 200 km/h, vid ́ eos AC pour cas extreme, puis preuve en ́ equation. 3 2 Doppler effect In addition to purely visual effects described in the previous section, an important acoustic effect can impact the sense of speed of a car, namely the well-known Doppler effect. The observed frequency of a source moving at velocity v with respect to a static observer is given by f ′ ( v ) = c c − v f, (4) where c is the speed of sound in the medium (here, the air). As a consequence, our brain intuitively knows that an object is moving fast if the difference between f ′ and f is large ( i.e. if the variation of the perceived pitch is large). Therefore, we assume that the sense of speed associated with a moving object depends on the change of frequency ∆ f = f ′ ( v ) − f ′ ( − v ) induced by its velocity, through the Doppler effect : ∆ f = c c − v f − c c + v f = 2 f cv 1 c 2 − v 2 (5) Hence, the magnitude of the change in frequency linearly depends on the base pitch of the sound. This is why high RPM engines seem faster to our ears : their change in frequency when they pass by the camera is larger than for low-reving cars passing by at the same speed. Figure 3 illustrates the variation of pitch from a simulation of two cars passing by a camera on located the side of the road. The transition from high- to low-pitch has the same form in both cases, but the high-reving car induces a steeper frequency change to the ears of the observer. Figure 4 displays the same quantity for a given car, but with varying distance of the camera from the track. This time, the duration of the transition from high- to low-pitch is impacted. The further the camera is from the car passing by, the less the observer can sense the speed. Figure 3 – Doppler effect of a low-reving car (blue) and a car with twice as much RPM (red) passing by a camera on the side of the track. Time and frequency are in simulation units. 4 Figure 4 – Impact of the distance from camera to the track on the doppler effect of a car passing by a camera on the side of the track. Close camera is on the immediate vicinity of the track, middle camera is 3 car lengths away and far camera is 6 car lengths away. Time and frequency are in simulation units. 3 Conclusion In conclusion, current Formula 1 cars are extremely well suited to appear slow to any observer, despite being actually fast. Namely, they contain all the important features to appear as slow as possible : 1. They are large, thus their motion relative to the external markers appear slow. Moreover, the rate of change of their agular size is also slow. 2. The engine they use has a low pitch (for race cars) and, as a consequence, the rate of change of the frequency of their sound by Doppler effect is low, when they pass by an observer. Many commenters explain the use of low RPM engine by invoking the need for F1 to attract car brands that do not want to promote large displacement, noisy engines. 3. They are extremely stable (this may not be considered as a problematic feature, for security reasons). 4. They are filmed in a way that makes them as motionless as possible (again, for viability reasons, one may consider this point as essential to F1). Since only the first of all the above points has no clear justification 4 it seems urgent for F1 to adjust the size of the cars, especially given that it primarily impacts their overtaking capabilities, in addition to the poor sense of speed it provides. 4. Security issues can be tackled by adjusting the weight of the cars instead of solely adopting large crash structures. 5