Death by Caffeine: The Maths Part 1 METRIC

Death by Caffeine: The Math  Part 1 USA UNITS here.

The lethal dose for caffeine is about 150 milligrams per kg of body weight. While the average person’s caffeine consumption is around 200 milligrams a day, the Mayo Clinic advises against exceeding 500 to 600 milligrams per day.

This work titled Timing is Everything is by street artist ABOVE in London.

You may want this much energy but be warned, energy drinks can kill.

It would take a ridiculously huge number of ANGRY WOMBAT energy drinks to kill a 14 year old weighing, say, 48 kg. Nevertheless, some kids are more sensitive to caffeine than others and then much lower levels of consumption of energy drinks can be fatal. 

See Death by Caffeine: The Maths Part 2 METRIC

Here is the work (see below) TIMING IS EVERYTHING by street artist ABOVE in London showing the timing.

 

Death by Caffeine: The Maths Part 1 METRIC

Death by Caffeine: The Math  Part 1 USA UNITS here.

The lethal dose for caffeine is about 150 milligrams per kg of body weight. While the average person’s caffeine consumption is around 200 milligrams a day, the Mayo Clinic advises against exceeding 500 to 600 milligrams per day.

This work titled Timing is Everything is by street artist ABOVE in London.

You may want this much energy but be warned, energy drinks can kill.

It would take a ridiculously huge number of ANGRY WOMBAT energy drinks to kill a 14 year old weighing, say, 48 kg. Nevertheless, some kids are more sensitive to caffeine than others and then much lower levels of consumption of energy drinks can be fatal. 

See Death by Caffeine: The Maths Part 2 METRIC

Here is the work (see below) TIMING IS EVERYTHING by street artist ABOVE in London showing the timing.

 

Formula One Car Designers need Maths

In a recent article in The Guardian, UK Ian Wright, the chief engineer for vehicle dynamics with the Mercedes AMG Petronas Formula One team, said: “There’s definitely a shortage of the right people. What we’ve found is that somebody spot on in terms of the maths can’t do the software; if they’re spot on in terms of the software, they can’t do the maths.”

Mathspig looked up the Mercedes AMG Petronas Formula One website and found this ad:

Senior Mechanical Designer (or Design Engineer)

Knowledge of Catia V5, suspension systems, vehicle dynamics, hydraulic systems and composites would be an advantage. Flexibility in hours and approach is required, along with a positive ‘can do’ attitude and the skill to communicate effectively. The ability to work unsupervised and with a very high degree of drive and self-responsibility is essential.

Well, of course, mathspigs, you need a high level of drive to work in a Formula 1 team, but you also need maths. See Can a Formula 1 Car drive Upside Down?

There is a lot of maths in designing F1 racing cars.

Simple Maths

More @ racemath

to complex maths involving aerodynamics

More @ Build Your Own Racing Car

Formula One Design

The following video gives a very good insight into Formula One Car Design and Aerodynamics

Formula One Design Maths

Here is a grab of Formula One Design Maths from Formula1 Website:

The Bernoulli principle has a big role in the operation of the aerodynamic surfaces of an F1 car. The Bernoulli principle is expressed by an equation, which states that for a given volume of fluid, the total energy remains constant. This means that when a fluid is in relative motion, the energy is split into the ‘parts’. The sum of these parts will not exceed a certain value, which will remain constant as long as the external conditions do not change.

The three parts of the total energy are:

1)  The pressure energy within the fluid.


2)  The movement of the air (kinetic energy)


3)  The potential energy of the air (in this case, elevation)

This can be written as:

p + 1/2 r v2+ rgh = some constant

p = Pressure


r = Density of fluid


v = Velocity of fluid


g = Acceleration due to Gravity


h = Height of fluid above some reference point

Your average track is fairly level, so a race car will not have enough change in elevation to make the potential energy a variable, so we take this potential energy as a ‘constant’and therefore are able to remove it from the equation. This leaves us with:

p + 1/2 r v2 = some (other) constant

We can rewrite this as:

p + q = H

p = static Pressure


q = 1/2 rv2 = dynamic pressure


H = some (other) constant

This basically means that if the dynamic pressure increases, the static pressure has to decrease and if the dynamic pressure decreases, the static pressure will increase. This means that if we speed up a fluid, the pressure will fall.

CONCLUSION, mathspigs,

Formula 1 Car Designers need maths.

Can a Formula 1 car drive upside down? Can an ordinary car fly?

The 2010 Grand Prix is about to hit Melbourne next month so this week, mathspigs we are going to look at car aerodynamics. There are two factors in car aerodynamics. Lift(L) and Downforce(D)

LIFT (L)

Car designers didn’t worry about aerodynamics until the sixties when cars could go fast enough to experience aerodynamic lift, which naturally, reduced tyre traction.  Skirts are added to cars to not only reduce this lift but also create a ‘suction’ (Bernoulli Effect”) under the car.

Here is the Chevy ’69 Camaro from Camaro Untold Secrets.  At 115 mph ( 185 kph which is not only fast but over street speed limits!!!!!) it experienced a front Lift (L) of 375 lbs or pound force.

We’ll simplify the aerodynamics and assume this graph is a parabola as follows.

NB: the only units to use in this equation are L (lb force) and v mph.

Once you know this equation you can calculate the velocity required for a ’69 Camaro to leave the ground due to front Lift (Assume once the nose lifts the downforce no longer applies ie. equals zero.)

We know the weight of the ’69 Camaro = 3,675 lb.

So mathspigs if the ’69 Camaro can go fast enough so that the front Lift equals its weight, it will fly!  At what speed will ’69 Camaro fly?

Downforce (D)

The ultimate design in car aerodynamics is the F1 racing car.  The Downforce (D) on the car is created by the front and rear wings, which work in reverse to aeroplane wings pushing down on the car) and the underbody gap which crates ‘suction’ by the Bernoulli effect.

 

Williams FW31 weight including driver  605 kg

      

                

                                                                                                                                                                                                   Renaut R30 total weight 605 kg

                                

      

Toyota TF 109    weight 605 kg                                                                                                                                                                                                                                                       

                                                                                                                                                                                                                                          BMW Sauder C29    620 Kg

 

 

Ferrari F60    605 kg

Downforce is approx:

35% rear wing

25% front wing

40% defuser on underbody

While downforce equations are complex ( See Wikipedia ) they approximate to the following equation for a standard F1 car design:

Could the Downfoce (D) on a F1 car exceed its weight so that it could drive upside along a … very long tunnel? I’m thankful to New Scientist (Aerial Glue 20 Jan 2010) for this insight.

Now mathspigs you have the mass of F1 car above so you can calculate the speed at which a typical F1 racing car could drive on the roof of a tunnel glued to the ceiling by its own downforce.

NOTE: This equation only works for a limited range of car mass, m. You can’t reduce m by dumping bits of the car. Likewise, if you add bits to the car to increase m eventually the aerodynamic constant, k, will change.

Does the weight of a driver make a difference?

Mathspig did stand in the pits in the Australian Grand Prix in Adelaide in the ninties ( with a borrowed ticket) not far from Ayrton Senna (Right. Tragically killed in 1994) and I was shocked to see how small he was. His height is recored at 171 cm but that is Mathspig’s height and he was shorter.  Today while some F1 drivers are over 6 ft (183 cm) including Australia’s Mark Webber (Right) most are not tall and, therefore, not that heavy.

When the KERS (Kinetic Energy Recovery System), which stores braking energy, was introduced 2009 drivers lost weight to accommodate system.

Nico Rosberg 76 kg to 66 kg

Kubica 78 kg to 70 kg

Heidfeld  56 kg to 59 kg

While Trolli, Hamilton and Vettel reduced their weights to 64, 67 and 62.5 kg respectively.  More info

Typically, a driver will lose 5 kg just competing in a Grand Prix.  IF the driver dropped 15 kg would that effect the upside down speed of an F1 racing car?  Drop the mass (m) value above and see if it makes much of a difference.

Or, instead, if your School Principal was driving the F1 racing car ( Assume an average  F1 driver weighs 65kg. How much heavier is your Principal to an F1 driver? Guess.) Increase the mass (m) in the above equation by this amount and you can calculate the speed  at which your school principal and F1 car would drop off the tunnel ceiling.

Meanwhile, even Mythbusters hasn’t tested this stick to the ceiling theory. Why?

Even the slightest bump on the ceiling could disrupt the underbody ‘suction’ and down goes the $zillion car and driver upside down and at speed.

This hasn’t stopped some Youtube mockups of F1 cars driving on the ceiling!!!