### Economical Driving - The Physics

Cars - The Real Purchase Price

Economical Driving

Fast Driving And Increased Fuel Cost

Fuel Consumption Ratings

Head Injury

Improvement

Internal Combustion Engine

A heavy large boulder requires a great deal more energy to

**than a lighter stone. This demonstrates the property of inertia. Inertia relates to a rotation motion, but as a body moves horizontally while being pulled down by gravity the vectors combine. The result is similar in principle to the orbit of a satellite around a planet. So it is with a vehicle. The forward motion and gravitational downward motion that is dependent on the weight (mass) of the vehicle.**

*initiate movement*
A tank has a continuous track and this spreads the load

so minimising the downward gravity influence (friction)

A small lightweight car will require less energy to start movement than a heavy one and anyone who has ever pushed a car will appreciate this. The kerb weight defines the gross standing weight of a vehicle without passengers or cargo, and can be anything between

*and*

**1***. The M1 Abrams battle tank weighs in excess of*

**2.5 tonnes***. Once a vehicle is*

**60 tonnes****it acquires momentum and is essentially a measure of**

*moving***. Energy is consumed to initiate this movement and requires the same energy to stop the motion. This is generally braking, but will also incorporate drag and is the result of gravity pulling down on the vehicle and the resulting friction of the tyres with the road. This resistance to movement is ever-present so a heavy vehicle requires a greater amount of energy just to maintain movement. The drag forces also include wind resistance once in motion. The faster the forward motion, the greater the resistance to this motion:**

*resistance to stopping***and**

*friction of the tyres on the road**caused by static air. On a windy day, the energy requirement changes and depends on whether a head-wind, following-wind or cross-wind applies.*

**resistance**Kinetic energy relates the mass and speed of an object and this relationship is not linear, but a square function. If the speed is

*, the KE is*

**doubled****.**

*quadrupled**the velocity and the KE is increased by*

**Three times****. To provide this force, liquid (or gaseous) fuel is consumed and converted into a different form with the production of energy. Not an efficient process. On a windless day, a**

*9 times**vehicle propelled from*

**2.5 tonne****in**

*0-60kmph**will use an enormous quantity of fuel when compared to a*

**5 seconds****vehicle accelerated from standing to**

*1 tonne***in**

*60kmph**and will consequently require much less*

**10 seconds***. The problem here is what speed is the base*

**'fuel'***so allowing the estimate of*

**x1****or**

*x2***? The vehicle**

*x3**figure that has a*

**mpg***speed does not allow the*

**defined****at**

*mpg***that speed to be estimated. A heavy**

*half***and large engine (**

*(2.5 tonne)*

**+***) moving at*

**3****L****in top gear may be just**

*60**kmph**. A smaller engine (*

**"ticking over"**

**1.2***) will generate much*

**-1.4****L****and will consume more fuel even though the vehicle may only be**

*higher rpm***. The fuel consumption figures to achieve this speed (**

*1 tonne**) is not available and it may be*

**60****kmph****,**

*easy***or**

*intermediate*

**hard****.**

*acceleration*

**The figure is meaningless when such a variety of engine**

**sizes and undefined driving conditions apply**The

*M1 Abrams battle tank accelerated to*

**60 tonnes****uses a**

*30kmph**. These tanks*

**tremendous quantity of fuel**

*do not use a clutch**(the intense friction would cause it to burn out)*and the connection between the engine and gears is simply

**or**

*on***.**

*off*Hard acceleration and high

**will result in a very high rate of consumption. A more gentle velocity rate increase (acceleration) will produce much improved economy. At constant velocity, a**

*revs***journey at**

*5km***will take**

*30kmph**(approximately, since the relatively short time for*

**10 minutes***is ignored), at*

**0-30, 60, 90kmph***takes*

**60kmph****and travelling at**

*5 minutes***will take**

*90kmph**. Clearly, the greater the speed, the shorter the journey time. The fuel consumption will increase from*

**3.33 minutes***to*

**x1****to**

*x4***, respectively**

*x9***. A journey may be**

*(30 -> 60 -> 90)**quicker, but the cost in fuel increases (at least) by a factor of*

**x3***. However, the base speed will clearly make a*

**x9***difference:*

**major****->**

*30**kmph*

**60****is**

*kmph**and ->*

**x2**

**90***is*

**kmph***if*

**x3***k*

**30****is the base speed. If**

*mph*

**60****is the base speed then**

*kmph***is**

*90kmph***this value and**

*x1.5*

**not***. As an instance the Bentley W12*

**x3***has a published fuel economy of*

**(Continental Flying Spur)**

**17***at*

**mpg**

**60***(*

**mph**

**96***) and so this can be converted to*

**kmph**

**34***at*

**mpg**

*30***or around**

*mph*

**7-8****at**

*mpg*

*90**(*

**mph**

*60***->**

*mph*

**90***=*

**mph****velocity, but**

*x1.5***KE**

*x2.25**=*

*1.5 x 1.5***square function). The picture can be massaged to provide a**

**answer. This single example illustrates the essentially meaningless nature of such figures when comparing**

*'best'***vehicles.**

*very different*Simplistically, if a car capable of

**required**

*50mph***, a similar (size/weight) would need at least**

*50**bhp*

**100**

*bhp**to reach*

**(x2)**

**100**

**mph****. But to move at**

*(x2)*

**200**

*mph**power in excess of*

**(****x4)***would be necessary. An additional*

**800bhp (x16)****to a top speed of**

*50**mph*

**250***would require*

**mph****. A small increase of**

*1250**bhp (50x16)**to*

**10****mph****(+5.16%)**

*260**would need*

**mph**

*1350bhp***. This may seem to be a**

*(+8% = 50x27)***of just**

*modest increment*

*100**bh**p***, but is all that is necessary to power the vehicle to initially**

*(+8%)*

*100***. The engine that powers the vehicle to the highest speed adds significantly to the kerb weight. Power is a requirement not just to increase the overall velocity of the car, but also propel the increase in weight to this speed.**

*mph*- In other words, to increase the speed from
to*100mph**260**mph*requires a power (and concomitant fuel) increase of*(x2.6)***100**to**bhp***1350**bhp*.*(x13.5)*

**50***->*

**mph**

**100****mph**

**(x2)**=*Power: 50 x 4***200***bhp*increase in speed,**100%**increase in power**400%**

**50***->*

**mph**

**200****mph**

*(x4)*=**Power: 50 x 16****800***bhp*increase in speed,*400%*increase in power*1600%*

**50***->*

**mph**

**250****mph**

*(x5)*=**Power: 50 x 25****1250***bhp*increase in speed,*500%*increase in power**2500%**

**50***->*

**mph**

**260****mph**

*(x5.2)*=**Power: 50 x 27****1350***bhp*increase in speed,*520%*increase in power**2700%**

So, to increase the top speed by

*from*

**x5.2***to*

**50****mph**

*260**mp***requires a**

*h***power output of**

*x27**to*

**50****bhp***. The increase in engine size and weight conspire to create a huge increase in fuel cost. Crudely, up to*

**1350****bhp***the volume (litres) of fuel. Reaching a high speed requires energy, but maintaining any velocity needs fuel and power to overcome the resistance caused by movement through the air (the value of the square of the speed) and the downward influence of gravity: the heavier the vehicle, the greater the downward force and the consequential increase in friction between the tyres and road surface.*

**x27**The acquired momentum will require efficient braking to slow and stop the moving vehicle. The faster the moving vehicle, the heavier the braking required as the momentum

*is that much greater. The major consequence of a heavier vehicle arises from the combination of drag forces:*

**(mv)***and*

**wind resistance****on the road, which are in opposition to maintaining the achieved velocity after acceleration becomes**

*tyre-friction*

**zero***(constant velocity)*. Wind resistance increases dramatically (square function) as speed increases as does the

**: tyres get hot**

*friction**at speed (the*

**, the**

*faster***). These forces will slow the vehicle to an eventual standstill unless energy**

*hotter***is applied and all this assumes a flat road: ie**

*(fuel consumption)**and*

**no upward****inclination (hills). As a vehicle moves downward, the potential energy changes into kinetic energy and does work. Momentum =**

*no downward***and the greater the weight**

*mv**of the vehicle, the*

**(mass)****the momentum for a**

*greater**. Movement*

**given speed****will require an energy input (acceleration) to maintain a constant velocity as gravity pulls the vehicle**

*uphill***onto the ground increasing**

*down**and raising the potential energy while decreasing the kinetic energy. The drag in opposition causes a decrease in the velocity (deceleration) An acceleration will be required to maintain constant velocity. Fuel load goes*

**tyre friction****considerably.**

*UP*As an economy comparison for the

*journey, the only obvious difference in the energy requirement between the*

**5km***or*

**30kmph, 60kmph****journey is the acceleration time: slightly longer to achieve a higher speed. The fuel consumption when the steady speed has been reached will appear to be the same for two comparative vehicles**

*90kmph***and**

*(1 tonne***. It isn't. To maintain progress, energy must be consumed and the heavier the vehicle, more energy is necessary.**

*2.5 tonnes)*If the speed is raised from

*to*

**30 kmph**

**60kmph****, for a**

*(+100%)**vehicle the KE increases from*

**1 tonne**

*1*30*30**joules*

**(900***to*

**)**

**1*60*60***joules*

**(3600****. A**

*)***increase. Increasing the acquired velocity to**

*fourfold*

*90kmph***the energy requirement changes considerably:**

*(+50%)***joules**

*1* 90* 90**joules*

**(8100***and is a*

**)***increase when compared to the*

**9 times****.**

*slower speed**increases by*

**Speed****and**

*3 times**goes up by*

**fuel load****. Energy increase is**

*9 times**to*

**900***to*

**36****00****joules. The change is actually in the ratio**

*8100***or a square function of the velocity for a given mass. If the car is heavier**

*1:4:9***then the energy requirement is substantially greater: the KE increases from**

*(2.5 tonne)*

*2.5 * 30 * 30***joules**

*(2250**to*

**)**

*2.5 * 60 * 60***joules**

*(9000**to*

**)**

*2.5* 90*90***joules**

*(20250**. Again an increase of*

**)****when compared to the slowest speed or just**

*1:4:9***the energy requirement compared to the next lowest speed (**

*x2.25***=**

*90kmph**joules ->*

**20250****=**

*60kmph***joules). However, for true comparison between the**

*9000***and**

*1 tonne**vehicle the energy increase is potentially) rather different than it*

**2.5 tonnes***:*

**'appears'**Although the increment is still

**for each weight, the difference between the two cars of different weights and**

*1:4:9***is actually**

*low/high speed**joules and*

**900****joules. This shows that a heavier**

*20250**vehicle driven at*

**(x2.5)***speed*

**x3****of the lighter vehicle**

*(90 kmph)***requires**

*(30kmph)***the energy from fuel:**

*22.5 times**at*

**2.5 tonnes***requires*

**90kmph****the fuel load of**

*x22.5**at*

**1 tonne****. Another way of stating this is that at constant speed over a fixed distance the fuel demand for a**

*30kmph**vehicle is potentially*

**2.5 tonne****greater than the**

*22.5 times**vehicle depending on the driving speed and conditions. This may be basic physics, but the scenario itself is complex and very easily massaged.*

**1 tonne**

*(Dynamique: 1.2 16V 3dr hatchback)***1090**(kerb weight),**kg**,*47**mpg*,*73**bhp**50L*4.54*Theoretical distance/tank = 47 * 50/**= 518 miles*,*Top speed = 102mph**0-60**mph*=**[59% potential]***12.6**seconds*Car tax:**139***g/km CO2*

**(Studio: 1.4 16V 3dr hatchback)**-
**1150**(kerb weight),**kg**,**42****mpg**,*73**bhp**55L* *Theoretical distance/tank = 42 * 55*4.54*/**=**509 miles*

*Top speed =*,*102mph**0-60**mph*=**[59% potential]****13.6****seconds**- Car tax:
*158**g/km CO2*

*(1.4 16V S 3dr hatchback)***1139**(kerb weight),**kg**,*44**mpg***90**,*bhp**50**L**Theoretical distance/tank = 44 * 50*4.54*/**=***485 miles**=*Top speed*,*112**mph**0-60**mph*=*[54% potential]**13.7***seconds**- Car tax:
**152***g/km CO2*

**(4.4 xDrive X6M 5d Auto)****2305**(kerb weight),**kg**,*20**mpg*,*547**bhp**85**L**Theoretical distance/tank = 20 * 85*4.54*/**= 375 miles*

=*Top speed*,*155**mph**0-60**mph*=*[39% potential]**4.5**seconds*- Car tax:
*325***g/km CO2**

**(6.2 V8 Adventure 5d Auto)**-
**2850**(kerb weight),**kg**,*16**mpg*,*392bhp**121**L* *Theoretical distance/tank = 16 * 121*4.54*/**= 426 miles*,*Top speed = unknown**0-60mph = 7.6 seconds*

- Car tax:
*412**g/km CO2*

**(Continental Flying Spur)**-
**2475**(kerb weight),**kg**,*17**mpg*,*601bhp**90**L* *Theoretical distance/tank = 17 * 90*4.54*/**= 337 miles*,*Top speed = 200mph**0-60mph**[30% potential]**= 4.5 seconds*

- Car tax:
**396***g/km CO2*

- The Renault Clio, Ford Focus and Peugeot 207 have very similar statistics. The BMW X6M, Hummer H2 and Bentley W12 are included for comparison of high performance and very poor economy and demonstrates that there has
or consider speed restrictions in the UQ (aka UK) Ltd. The objective has always been to*never been any attempt to reduce petrol consumption*and this is very clearly demonstrated reviewing the car tax levied*maximise revenue*.*(March 2010)*

- Considering these figures alone it appears that the Peugeot 207
requires a**(1.4)**increase*23% bhp*to produce a similar performance to the Renault Clio**(90bhp)**or Ford Focus**(1.2, 73bhp)**. The Renault has the smallest engine*(1.4, 73bhp)*and is possibly a reason for it being the lightest of the three, but this is traded off against the potentially lower revving engine of the Peugeot 207*(1.2)*at a comparative speed:**(1.4)**against**59%**.*54%*

- The BMW X6M is
**more than**the kerb weight of the Ford Focus or Renault Clio and for its performance statistics requires an engine that produces**twice**the power output*x7.5*. The fuel consumption figures support this:*(547 v 73bhp)*. This comparison is at*42 - 47mpg v 20mpg*, but the potential**60mph**shows that this**(155mph)**will**20mpg**considerably (the*drop*is not known).*rpm*

- The Hummer H2 is a tank, but even so has greater potential than the Bentley W12, which has
regardless of its potential performance. At nearly its top (published) speed (potential =**truly absurd fuel economy**) at**200mph**, the fuel economy (theoretically) plummets to*180mph*the*1/36th*figure (*30mph**speed*, KE =**x6**). Even at**x36**it is only*60mph*.*17mpg*

**This is probably the non-disclosed reason why such performance cars**

**are allowed to be built since they can never in reality be driven at**

**such speeds without requiring frequent refuelling**Performance statistics for diesel engines appears to compare well with petrol powered cars, claiming

**driving, but at an**

*42mpg for combined**and*

**unspecified speed***(*

**declared rpm***are assumed to be*

**revs***). The*

**per minute****V6**

*2993cc (3L)**turbodiesel engine delivers*

**24v***@*

**271bhp***,*

**4000rpm**

**443***lb ft*@

*. The standing-start acceleration to*

**2000rpm****=**

*62**mph*

**5.9****and a**

*seconds**(electronically governed) of*

**top speed**

**155***. This car has a kerb weight of*

**mph****and emissions at**

*1820kg***. At**

*179**g/km CO2*

**4000****what is the speed? The potential may be**

*rpm***, though what**

*155mph**are produced at this*

**rpm****? Electronically governed implies there is more theoretically available and so the**

*'top speed'**by themselves do not impart any significant information. Note: mixing imperial and metric units.*

**rpm**- Describing a car this way makes it sound like a strong performance, yet not declaring details of fuel consumption except
driving, which is*42mpg for combined*when presented as a single statistic.*absolutely meaningless*

- Why is the acceleration statistic
of a car so important? It is**(0-60mph)**__the__and simply means that the next__most__fuel uneconomicis more quickly reached. And a longer wait until the**red trafffic light**- DA*following green light*