**This blog was originally published on Bristol Cycling's website. **

Our lives fundamentally rely on energy. It puts food on our table, gets us to and from work, powers our offices and factories. The more we use, the more money it costs us. Our demand for it causes wars, our generation of it emits harmful gases.

Almost every issue 20mph raises is energy related and the answer to each, along with many of our urban challenges, can be found by looking for the lowest energy solution.

Energy dictates the severity of a collision, how much fuel is burnt to move somewhere and the volume of emissions that activity will release. The more energy we put through car components and the road surface the quicker they will break and wear out. The faster a vehicle moves the more noise it generates.

Yet energy is rarely mentioned. Despite apparent concerns over climate change and air pollution, sales of energy-hungry SUVs are soaring, up 24% across Europe this year and on course to become the most common cars on our roads.

So in this time of “fake news” and manipulation of facts, what better way to argue a case than with some basic physics. Just as keen cyclist Albert Einstein might have done.

*The figures in these calculations use the Nissan Qashqai, the most popular SUV on Britain’s roads, with a kerb weight of 1419kg and a Coefficient of drag (Cd) (how well it slips through the air) of 0.32 and a rather hefty frontal area (A) of 2.6m2. All the energy figures are given in Watt-hours (Wh) and kilowatt-hours (kWh). See some useful comparisons. All working out is shown at the foot of the page.*

Probably the most common argument in favour of 20mph is a safety one and it’s a very sound assumption.

A driver seeing a danger travelling at 30mph would have travelled 9 metres before they even pressed the brake pedal and another 14m to come to a stop. At 20 mph the overall the stopping distance is half that at 30. This makes a collision less likely in the first place.

The kinetic energy of our car travelling at 20 mph (8.94m/s) is 15.7 Wh. If the vehicle didn’t stop in time, this would be the energy felt by the object it hits. Increase this speed by 50% to 30 mph and the kinetic energy goes up by 125% i.e. it more than doubles to 35.4 Wh. To put this in comparison, the energy of a 90kg cyclist at 20 mph is 0.9 Wh and a 70kg jogger at 5mph, 0.05 Wh.

These figures have formed a key part of Sweden’s Vision Zero Strategy* , *which puts the energy of vehicles and their impact on humans as one of the key focal points. It is research from this that influenced the THINK! campaign in the 90’s. The principles behind this message are summarised in the graph below. As vehicle speed increases the consequences of injuries sustained in a collision dramatically increases.

Figure 1 – Graph showing the change in speed of a vehicle against the injury consequences (Nillson)

In Bristol, thanks to 20mph limits, there has been a reduction in the number of fatal, serious and slight injuries from road traffic collisions. Casualties avoided per year are 4.53 fatalities, 11.3 serious injuries and 159.3 slight injuries.

One of the main arguments against 20mph is that people think they are getting delayed and their journeys are taking longer. This might be the case if we were driving on long straight empty roads (like in the car adverts), but Bristol is hardly that.

The animation below shows the principles of the concertina effect (created to show the benefits of vehicles with sensors to control their distance to other vehicles). The greater the speed difference between drivers on a stretch of road, the more likely it is that this traffic behaviour will happen, as is demonstrated in the lower animation. Once this happens, traffic backs up, even though the road ahead might be clear.

Figure 2 – Animation showing the concertina effect (source: CSAIL)

The concept is explained in this article and the principles are demonstrated in a study on Helsinki 20 and 25mph speed limit zones which found traffic flow improvements.

At peak times within the 1-mile radius of central Bristol, average driving speeds are just 8mph. Even 5 miles out of the city this only increases to 12mph. Driving at 30mph not only means a journey takes longer, but more of it is spent accelerating, braking or stopped in a queue.

Once upon a time, it was assumed (in the UK anyway) that lower speeds result in higher fuel consumption, due to the typical speed/fuel consumption profile of an internal combustion engine (ICE) car in a straight line on an empty road. This myth has largely been disproved.

*Here’s why:*

As Bristol Cycling highlighted last year, simple physics dictates that halving speed reduces energy consumption 4 fold. Because of the staggering inefficiency of an ICE (a minimum of 85% of every a tank of fuel is lost as heat and does nothing to move a car forward), driving at a steady speed a vehicle has to overcome rolling resistance from the tyres on the road, and drag from the air. The energy to overcome rolling resistance is constant no matter how fast we go, however, drag is cubed with velocity. A 50% increase in speed means energy to overcome air resistance more than doubles.* *This is summarised in the figure below:

Figure 3 – Simple theory of car fuel consumption (energy per distance) when driving at a steady speed. Assumptions: the car’s engine uses energy with an efficiency of 0.25, whatever the speed (sewtha)

To accelerate the vehicle up to speed we need to give it kinetic energy (KE). KE is also squared with speed. So to reach double the speed requires 4 times the energy.

If our vehicle was travelling in space *(which is a vacuum)* it would keep going until it hit something, however because of air and rolling resistance it needs constant energy input to overcome these.

Figure 4 – Forces acting on the vehicle as considered in calculations

For a car driving 16km (10 miles) across town with 25 stops and starts, we can break the journey into equal 640-metre portions for simplicity. If the vehicle accelerates up to 30mph instead of 20mph it needs an additional 21.7 Wh per acceleration. Because ICE cars are at best 25% efficient (for urban driving 15% might be a more reasonable estimate) this is multiplied by 4 to give 86.8 Wh. A litre of petrol contains 9.7 kWh of energy, which equates to an additional 8.9ml of petrol per stop and start. At £1.27 per litre of fuel that’s an extra 1.13 pence per acceleration.

Figure 5 – infographic indicating fuel savings of a journey at 20 mph and 30mph

Factoring these figures up to the full journey is a full 28p saved on accelerations alone. In both directions, the total fuel savings of only travelling at 20 are equivalent to around a pint of fuel. Further extrapolating this calculation to all 261 working days in 2018, savings from travelling at 20 instead of 30 are a staggering £196 or an equivalent energy consumption of 1495 kWh. Which is similar to the electricity consumption of a single person household for a year.

For hybrid cars, lower speed limits allow the car to run on the battery more often, further reducing fuel consumption.

Lower fuel consumption is not directly proportional to reduced exhaust emissions due to the complexities of ICEs, however, an in-depth study in London found 20mph did reduce vehicle emissions, again mainly because the lower speed is more conducive to less erratic, smoother driving which reduces exhaust emissions. It also highlights that changes in average speed and accelerating and decelerating behaviours will be beneficial to non-tailpipe emissions of particulate matter, discussed in greater detail in the next section.

But what about climate change? Every government in the previous 20 years has told us climate change is the greatest threat we face and then puts it to the bottom of the list or takes it off altogether. In the previous two elections, it has barely been mentioned. It’s seen as a nice to do, maybe if one day the world is rich enough. Yet the costs of inaction are already staggering and will only grow. The chances of us meeting the non-binding Paris agreement limiting temperature rises to 2 degrees is small and it is now predicted that 3 degrees will be the likely minimum temperature rise. To put it in perspective, a 5-degree average temperature drop would put us in a full-scale ice age. Action has never been more urgent.

Bristol City Council lists an increase in CO2 emissions as a risk of a “Clean Air Zone” (CAZ), as people might (and are encouraged to) simply swap diesel cars for petrol. 20mph limits reduce CO2 emissions. The national institute for clinical excellence (NICE) recommends physical measures to encourage 20 mph adherence. The Autonumber Plate Recognition (ANPR) cameras proposed for the CAZ could be used for this.

Potholes are a pain for cyclists and motorists. We hear a lot about the terrible crashes they cause and the damage they do to vehicles, but what about the cause of them?

The fourth power law is well-established theory for calculating the effect vehicle weight has on road damage. A 50% increase in axle load results in a five-fold increase in calculated structural wear.

Our car with an average UK person (76.9kg) does **53,643 times** the damage of the same person on a (very heavy) 20kg bicycle, rolling over the surface of the road.

Even a 2,250kg Tesla Model S compared to a 1384kg average car, does nearly 6.5 times the damage to the road.

*But what about speed?*

As just mentioned, the energy in our car at 30mph is more than double that of the same car at 20mph. This means the energy, which dissipates through the brakes, tyres and roads is greater, causing more wear.

Over the course of a year of this article’s 16km commute* , *stopping and starting to and from 30mph is an extra 436 kWh, over 3 times the energy of the same journey at 20mph.

Figure 6 – The composition of tyre and brake wear in terms of various metals, ions, and elemental and organic carbon. Graphic from wattsthecost.info with data from EEA emissions factors.

Road, tyre, brake and engine wear all form “non-exhaust emissions”. These are breathed in by people, get mixed up in roadside vegetation and sweepings, such as leaves resulting in them being landfilled instead of composted or burnt for energy. Plastic from tyres even contributes to the growing burden in our rivers and oceans.

Less wear associated with 20 mph means not having to change brake pads, clutches and tyres as often. It also means safer streets with fewer potholes and less money needed by cash-strapped local authorities to repair them. It is estimated that to fix all roads in the Bristol area would cost taxpayers £1.2 billion. That would be an additional £10,000 for each of the 100,000 council tax payers in Bristol.

It’s estimated that the annual social cost of urban road noise in England is £7 to 10 billion. This places it at a similar magnitude to road traffic collisions (£9 billion). The WHO estimate noise to be the second biggest cause of environmentally related health problems. Road noise is one of the biggest contributors to urban noise pollution.

How can 20 mph reduce noise?

Put simply noise is wasted energy, so less energy involved moving along our roads means less noise generated.

The graph below shows a 10db increase between 30km/h (20mph) and 50 km/h (30mph). In terms of human ear perception, 10db is equivalent to a doubling of the noise level. If you turned a sound system up by 10db we would perceive it as the volume doubling.

A German study found the introduction of 30 kmh (20 (mph) zones into residential streets allows a reduction up to 3 dB(A). Another concluded a similar reduction. A 1999 Swedish study found that having an urban environment with combined 50kph (30mph) and 30kph (20mph) zones produces a more “jerky” traffic flow than blanket 30kph (20mph) and consequently more noise (2-4 db increase).

Figure 7 – Engine noise and rolling noise as a function of speed (RAC Foundation)

Enforced 20 mph limits would have a dramatic effect on the constant hum people living near busy roads hear throughout the day and night.

Figure 7 – Einstein riding his bike

Einstein was an avid cyclist. Not a for weekend sports, but as a means of transport to get around his hometown. He is famously quoted as saying the theory of relativity was conceived whilst riding his bike. We don’t know for definite, but like most other cyclists we are sure he would rather have shared the road with cars moving with half the energy, pumping out fewer fumes and doing less damage to the road.

The greatest energy benefit 20 mph can have is if people feel safer cycling on our streets they may decide to leave their hopelessly inefficient automobile at home!

The Bristol 20 mph consultation ends on the 31st August 2018. Make sure you register your views https://bristol.citizenspace.com/city-development/20mph-limits-review/ and don’t forget to mention the importance of energy.

An infographic summarising this article is available here.

A huge credit to the late Sir David MacKay for his book “sustainability without the hot air”, which helped with the calculations carried out here. This outstanding piece of work is available as a free download: http://www.inference.eng.cam.ac.uk/sustainable/boo... visit pages 254 to 260 for more detail on the basis for these calculations.

**Drag energy (Joules)** = 0.5 x density of air (kg/m3) x drag coefficient (CdA) x velocity (m/s)3

**Kinetic Energy (Joules)** = **Energy lost in Braking (Joules)** = 0.5 x mass of car (kg) x velocity (m/s)2

**Rolling resistance (Joules)** = Coefficient of rolling resistance (Crr) x (gravitational constant (9.81) x mass (kg) x Velocity (m/s)

1000 Joules (J) = 0.27777 Watt Hours (Wh)

Energy (Wh) = Power (W) x time (hours)

Average weight of person = 76.9 kg (source: bbc)

Weight of the best selling UK SUV (Nissan Quashqai) = 1419 kg (source: Topgear)

Coefficient of drag of a Nissan Quashqai (Cd) = 0.333

Frontal area of a Nissan Quashqai (A) = 2.6m2

Density of air = 1.3 kg/m3

Gravitational constant = 9.81 m/s2

Energy in 1 litre of petrol = 9.7 kWh (source: sewtha)

Coefficient of rolling resistance of a typical car tyre = 0.01 (source: engineering toolbox)

**Reducing collisions**

Energy in a moving car (J) = 0.5 x mass of car (kg) x velocity (m/s)2

Energy in a moving car at 30 mph (13.4 m/s) = 0.5 x 1419 x 13.42 = 127,611 Joules

Energy in a moving car at 30 mph (13.4 m/s) = 127611 x 0.0002777 = 35.4 Wh

Energy in a moving car at 20mph (8.9 m/s) = 56716 x 0.0002777 = 15.7 Wh

**Reducing fuel consumption**

For a journey of length 16km with 25 stops and starts split evenly across the journey

Each stop and start section is 16000/25 = 640m

Steady acceleration rate of a car = 2m/s2

Acceleration distance for each stop/start (m) = 0.5 x (target speed (m/s)2 – current speed (m/s)2)/rate of acceleration (m/s2)

Acceleration distance to 30 mph (m) = 0.5 x (13.42 – 02)/2

Acceleration distance to 30mph (m) = 44.97 m

Acceleration distance to 20 mph (m) = 19.98 m

Acceleration time to 30 mph (s) = 13.4/2 = 6.7 s

Acceleration time to 20 mph (s) = 8.9/2 = 4.4 s

Steady braking distance from 30 mph (m) = 25 m (adapted based on emergency stopping distances in from RAC)

Steady braking distance from 20 mph (m) = 12m (adapted based on emergency stopping distances in from RAC)

Braking deceleration rate from 30 mph (m/s2) = (target speed (m/s)2 – current speed (m/s)2)/2 x braking distance (m))

Braking deceleration rate from 30 mph (m/s2) = (02 – 13.42)/2 x 25) = 3.6 m/s2

Braking deceleration rate from 20 mph (m/s2) = (02 – 8.92)/2 x 12) = 3.333 m/s2

Cruise distance at 30 mph (13.4 m/s) = 640 – (44.97+25) = 570 m

Cruise distance at 20 mph (8.9 m/s) = 640 – (19.98 + 12) = 608 m

**Acceleration energy = **Kinetic Energy (Joules) + Drag energy (Joules) + Rolling resistance (Joules)

**Cruise energy = **Drag energy (Joules) + Rolling resistance (Joules)

**Braking energy = **Kinetic Energy (Joules) – Drag energy (Joules) – Rolling resistance (Joules)

Acceleration energy to 30 mph (13.4 m/s) =

Kinetic Energy (J) = 0.5 x 1419 x 13.42 = 127,611 Joules +

Drag energy (J) = 0.5 x 1.3 x 0.333 x 2.6 x 44.97 x (13.42) +

Rolling resistance (J) = 0.01 x 1419 x 9.81 x 44.97

= 127610 + 4556 + 6257 = 138,423 J

Acceleration energy to 30 mph (Wh) = 60,397 x 0.000277 = 38.1 Wh

Factoring in efficiency of engine (25%) = 38.1 x 4 = 152.4 Wh

Acceleration energy to 20 mph (8.9 m/s) =

Kinetic Energy (J) = 0.5 x 1419 x 8.92 = 127,611 Joules +

Drag energy (J) = 0.5 x 1.3 x 0.333 x 2.6 x 19.98 x (8.92) +

Rolling resistance (J) = 0.01 x 1419 x 9.81 x 19.98

= 56716 + 900 + 2781 = 60,397 J

Acceleration energy to 20 mph (Wh) = 60,397 x 0.000277 = 16.78 Wh

Factoring in efficiency of engine (25%) = 16.8 x 4 = 67.1 Wh

Cruising energy at 30 mph (13.4 m/s) =

Drag energy (J) = 0.5 x 1.3 x 0.333 x 2.6 x 570 x (13.42) +

Rolling resistance (J) = 0.01 x 1419 x 9.81 x 570 =

57757 + 79323 = 137,080 J

= 38.07 Wh

With engine inefficiency (25%) = 38.07 x 4 = 152.3 Wh

Cruising energy at 20 mph (8.9 m/s) =

Drag energy (J) = 0.5 x 1.3 x 0.333 x 2.6 x 608 x (8.92) +

Rolling resistance (J) = 0.01 x 1419 x 9.81 x 608 =

84609 + 27380 = 111,989 J

= 31.1 Wh

With engine inefficiency (25%) = 31.1 x 4 = 124.4 Wh

Braking energy from 30 mph (13.4 m/s) =

Kinetic Energy (J) = 0.5 x 1419 x 13.42 = 127,611 Joules –

Drag energy (J) = 0.5 x 1.3 x 0.333 x 2.6 x 25 x (13.42) –

Rolling resistance (J) = 0.01 x 1419 x 9.81 x 25 =

127610 – 2533 – 3479 = 121,598 J

= 33.78 Wh

Braking energy from 20 mph (8.9 m/s) =

Kinetic Energy (J) = 0.5 x 1419 x 8.92 = 127,611 Joules –

Drag energy (J) = 0.5 x 1.3 x 0.333 x 2.6 x 12 x (8.92) –

Rolling resistance (J) = 0.01 x 1419 x 9.81 x 12 =

56716 – 540 – 1670 = 54,506 J

= 15.1 Wh

Total energy expended by engine for single stop start cycle at 30 mph= 152.4 + 152.3 = 306.1 Wh

Total energy expended by engine for single stop start cycle at 20 mph =67.1 + 124.4 = 191.5 Wh

Total energy expended on brakes, tyres and road from 30 mph = 33.78 Wh

Total energy expended on brakes, tyres and road from 20 mph =15.14 Wh

Total Petrol at 30 mph = 306.1 x 9.7 =788 ml

Total Petrol at 20 mph = 306.1 x 9.7 =493 ml

**Reducing Road and vehicle damage**

**4th power law**

ALEF = (Heavier Vehicle/Lighter Vehicle)^4

ALEF = (Nissan Quashqai with average passenger/Heavy bicycle with average rider)^4

ALEF = (1461/96)^4 = 53643 times as much damage

Road and vehicle wear

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