Hi dear friend,
1. This text is very interesting. Please read it until the end. Thanks!
2. ACTIVE SUSPENSIONS
1994: Who did permit the realisation of a GP in a track that had a
corner done at the speed of 270Km/h (remember Senna's Telemetry Data),
with a 5 meters long escape that ended in a wall without any tyre
before?
1994: First FIA KILLED Active Electronics. Next FIA KILLED 'Drive By
Wire' Systems. Next FIA KILLED ABS Systems. Next FIA KILLED Active
Transmissions. Next FIA KILLED Active Suspensions. Next FIA KILLED
RATZEMBERGER with -722g's during 13ms. Next FIA KILLED SENNA with -66g's
during 48ms.
In the case of Ratzemberger crash I considered a
Chassis_deformation=1.15m and Vcrash=325Km/h and in the case of Senna
crash I considered a Chassis_deformation=0.75m, Vcrash=225Km/h and
alpha_crash=30o.
Note that 1ms=10^-3=0.001 seconds and g=9.81 m/s^2 and the maximum
deceleration the Brain supports (without suffering irreversible
lesions), in the +Gx direction (frontal crash) or in the +Gy direction
(lateral crash), is -45g's during 50ms.
Note that a F1 car (Cx=0.81, Sx=1.5 m^2, c_friction=1.37, m=700Kg) at
the speed of 270Km/h needs 120 m of good track to reduce the speed to
76Km/h, the maximum crash speed in a frontal crash into a wall without
tyres before (see exercise1 bellow). Of course that this braking
distance is the minimum length that the Senna's escape should have. If
you want I can send you the Excel model that I used to calculate this
braking distance. Please tell me the format: Excel 97 or Excel 5.0-7.0.
Exercise1: Considering a frontal crash with Chassis_deformation=0.5 m
and a constant crash deceleration G=-45g, calculate the crash speed
Vcrash and the crash time delta_t. Note that we have
Chassis_deformation= Vcrash delta_t + ? G delta_t^2
and
delta_t= -Vcrash/G
Solution: Vcrash=sqrt(-2*Chassis_deformation*G)=76 Km/h, delta_t=47.8
ms.
Exercise2: Calculate the 'Lady Di' crash speed Vcrash and the crash time
delta_t considering a constant crash deceleration G=-40g and a
Chassis_deformation=1.75 m and that the 'Lady Di' crash was a frontal
crash.
Solution: Vcrash= 133 Km/h, delta_t=94.1 ms.
Exercise3: Calculate the number of lines of tyres Ntyres necessary to
save Ratzemberger considering very hard tyres with Gtyres=-37g and
tyres with a diameter of 1m.
Note that delta_t_tyres=(Vcrash_wall - Vcrash_tyres) / Gtyres,
Vcrash_wall=76/3.6m/s, Vcrash_tyres=325/3.6m/s and
Ntyres=Vcrash_tyres delta_t_tyres + ? Gtyres delta_t_tyres^2
Solution: Ntyres=11, delta_t_tyres=191ms=0.191s
FIA didn't know these numbers?!! I'm sorry FIA, you don't have any
excuse.
Congratulations FIA, you're the Serial Killer of the year 1994.
If FIA hadn't KILL Active Suspensions, perhaps today almost all
production cars would have Active Suspensions, that is, they would have
much greater corner speeds, that is, they would have much greater
driving insurance.
I'm Sorry FIA, you're nothing more than a Serial Killer.
Senna would say: A F1 est mesmo a precisar dum 25 de Abril Americana!
3. I still have a lot of things to say but I can't find the words. I'm
sorry, I'm crying...
4. Senna would say: FIA, CAPITULAS OU QUERES MORRER COM MILH?ES DE BALAS
NO CORA??O? FIA, VAIS REINTRODUZIR AS SUSPENS?ES ACTIVAS NA F1 J NA
PRXIMA TEMPORADA OU QUERES SER FUZILADA?
5. Senna would say: 1. ISOLAR A FIA. 2. CERCAR A FIA. 3. APERTAR O
CERCO AT QUEIMA ROUPA. 4. FIA, CAPITULAS? 5. SE N?O, FOGO!
6. Senna would say: Ai, FIA, Ai dos vencidos! Agora alm das suspens?es
activas, vais reintroduzir a Electrnica Activa, os Sistemas de 'Drive
by Wire', as Transmiss?es Activas e vais introduzir novos motores de 5
litros, pois eu j estou farto de andar a pisar ovos a 340Km/h! :-)
Note that assuming that a 5 litres V10 Ferrari engine would have a power
P=1917 HP (1HP=746 watt), assuming very little downforce, that is,
Cx=0.89 (remember that the Ferrari chassis is very very bad :) ),
Sx=1.5m^2, p_mec=0.15, we would have a top speed, Vmax, of
P (1-p_mec)= ? rho Cx Sx Vmax^3 Vmax=( 2 P (1-p_mec) / (rho Cx Sx) )^
1/3
Vmax= 414 Km/h !!!
7. I'm so sorry, FIA... Do you forgive me?!! :)
8. Ora bolas, se tivesse feito isto 4 anos o Senna estaria hoje a
experimentar o seu novo V10 de 6.9 litros de 3000 HP! I'm sorry Senna,
I'm sorry Ratzemberger...
Exercise4: Considering that Senna's car would have a Cx=0.81, Sx=1.5
m^2, p_mec=0.13 and rho=1.2 Kg/m^3, calculate the top speed Vmax of
Senna's car.
Solution: Vmax= 499 Km/h !!!
9. PRODUCTION CAR MAKERS: PLEASE LEARN SOMETHING WITH McLaren!
In F1 a better chassis means less drag with the same downforce. Once the
Drag is given by
? rho Cx Sx V^2 (1)
less drag means lower Cx (assuming the same speed V, the same air
density rho and the same frontal area Sx).
Once the downforce is given by
m g + ? rho Cz Sz V^2 (2)
the same downforce means the same Cz (assuming the same weight m, the
same speed V, the same air density rho and the same horizontal area Sz).
Once the Cx is related with the Cz by
Cx= Cx0 + k Cz^2 (3)
we conclude that a better chassis means lower Cx0 and lower k.
Mika told me the top speed, Vmax1, and the maximum deceleration
Gbrakes_top_speed1 of the German GP Qualification and the top speed,
Vmax2, and the maximum deceleration Gbrakes_top_speed2 of the German GP.
From these Telemetry Data I found that the McLaren chassis is
characterised by Cx0=0.57 and k=2.37.
Schumi told me the same Telemetry Data and I found that the Ferrari
chassis is characterised by Cx0=0.77 and k=4.89.
I don't know the Telemetry Data of the remaining teams, but I have the
feeling that the McLaren chassis is the best chassis (that is, has the
smallest Cx0 and the smallest k) and the Ferrari chassis is the worst
chassis (congratulations Schumi, you're the best F1 driver!).
In 1980 very few production cars have a Cx=0.30.
Today Opel Tigra, Audi A4, Audi A3 and Audi A6 have a Cx=0.28 (see the
text in the appendix).
Does this mean that the optimal Cx of a production car is 0.28?
Or does this mean that production car makers have lot of things to learn
with McLaren?
10. Cx=0.045, the Cx of an F-16 aircraft at the speed of 500Km/h.
11. Cx=1.8, the Cx of a motorbike.
12. PRODUCTION CAR MAKERS: PLEASE LEARN SOMETHING WITH FERRARI!
Once the Ferrari chassis is so bad, how to explain the good results of
Ferrari?
I have the feeling that the Ferrari engine has a much greater maximum
torque and a much more flat torque curve than the Mercedes engine.
This means that the Ferrari has more acceleration and, once the energy
efficiency is 'proportional' to the torque, the Ferrari has a smaller
fuel consumption (which means less fuel weight and so still more
acceleration).
Actual production cars energy efficiency is very small, around 0.25 at
the speed of 120Km/h, and the theoretical limit is 0.45 (see the text in
appendix).
This means that production car makers have lot of things to learn with
Ferrari!
13. SEMI-AUTOMATIC GEAR BOXES
Almost all production car drivers don't know the torque curve and the
relations of the gear box of their cars and so they don't get the
maximum acceleration in overtaking, which means less insurance in
overtaking.
A good automatic gear box will change gears at the right times (that is,
at the right RPMs) maximising the acceleration and so maximising the
insurance in overtaking.
The idea is 'pulling' the gear i until a RPM_i such that the RPM_i+1 at
gear i+1 is exactly equal to the engine RPM_maximum_torque.
For example, driving a Citro?n AX 1.1 we must 'pull' the second gear
until RPM_2=5250 RPM (that is 72Km/h) because the RPM_3 at 72Km/h in
third gear is 3750 RPM, which is exactly the RPM_maximum_torque of the
Citro?n AX 1.1. I think that the Citro?n Saxo 1.1 has a very similar
gear box and torque curve, so these results are also valid for the
Citro?n Saxo 1.1.
This means that a engine with a smaller RPM_maximum_torque will have a
longer life (Why?).
Of course that the Mercedes A140 engine will have a very short life!
(see next section to understand why!) :)
The main problem of the actual production car automatic gear boxes is
that they imply much greater mechanical losses (p_mec=0.45, p_mec is
defined by
P (1-p_mec)= ? rho Cx Sx Vmax^3 (4)
and production cars with manual gear boxes have a p_mec=0.25. Note that
these values of p_mec include tyres friction).
F1 Semi-Automatic gear boxes have a much lower p_mec=0.15 (including
tyres friction). So it seems interesting to adapt this technology to
production car automatic gear boxes!
14. MERCEDES: PLEASE LEARN SOMETHING WITH McLaren AND WITH FERRARI!
The new small Mercedes production car A140 is a disaster!
Senna would say: Mercedes, o teu A140 uma bela carro?azinha! :-)
The Mercedes A140 has a Cx=0.45, EE(120Km/h)=0.13, RPM_max_torque=5250
RPM and a fuel consumption of 12 litres in a course of 100Km done at the
stabilised speed of 120Km/h. :-)
This means that making a course of 100Km at the speed of 120Km/h is
heating the air with the heat produced by the energy contained in
0.87*12=10.44 Litres of fuel, which is about 10.44*37*10^6= 386 *10^6
Joules= 386 Mega Joules!
So, although the Mercedes A140 is the worst production car of its class
(small cars), it's very hot! :-)
If you like hot cars, buy a Mercedes A140! :-)
Note that a very small Energy Efficiency means a very small maximum
torque, that is very small acceleration in overtaking, that is the
Mercedes A140 is a very dangerous car! :-)
Senna would say: Mercedes, por favor interrompe a produ??o da tua
carro?azinha, imediatamente! :-)
The other Mercedes production cars are also a disaster and, of course,
very very hot! :) (see the text in appendix).
Senna would say: Mercedes, quando chegares aos
...
read more »
<snip>
FIA didn't KILL [sic] active suspension. It didn't originate in F1,
and development, such as it is, for road vehicles has continued
independent of what goes on in F1. It's just that what's practical on
a multimillion-dollar budget with a horde of engineers and mechanics,
to be driven only on a carefully-controlled course by an expert driver
might just not be practical for a production car.
<snip>
--
-Stephen H. Westin
Any information or opinions in this message are mine: they do not
represent the position of Cornell University or any of its sponsors.
