Monday, 1 December 2003

How to pull this Christmas!

With office Christmas parties now in full swing, and Christmas Day just around the corner, Woolworths has enlisted the help of a top engineer to develop a formula that will make those with a competitive nature jump for joy – you never need to lose a cracker-pull ever again.

Whether it’s board games, silly stories or cracker pulling, some people just have to win. If you always falter at quiz questions and are sick of being the butt of family jokes, just use the cracker-pull formula that boffins who work for Woolworths have developed, and you’ll never lose at cracker-pulling again!

The formula, developed for Woolworths by Dr Matthew Bennett, B.Eng., C.Eng., MIChemE , is based on a number of factors, all which contribute to the ‘perfect pull’. He spent hours in a laboratory testing over 200 crackers to come up with this formula – just don’t tell the rest of the family!

e = 11 C + 5Q

e = optimal angle for pulling the cracker

C = circumference of cracker barrel

L = length of cracker barrel section

Q = cracker "quality factor"

Dr Bennett obtained his first degree and PhD from Bath University, and is now a Senior Process Technology Engineer working for a high profile company.

Says Dr. Bennett, "I always remember as a child wishing I could beat my younger brother/sister at something.

Then while in Woolworths this idea just sprung into my mind as I spend my working life formulating mathematical solutions. By working with Woolworths on this, I feel as though I have finally got my revenge – what a great Christmas present to all kid brothers and sisters, a harmless way to get back at their siblings."

Nicole Lander, Head of Corporate Affairs, Woolworths said: "Most of us want to win when we pull a cracker. This is a guaranteed way to get one up over your brother, mum, colleague or friend to make sure you’re the one cracking the jokes over Christmas lunch or at the office party." Woolworths, which sells around 15 million crackers every Christmas, thinks this is a great idea and is considering adding the formula to some of its packaging for next year.
So how do we know that it really works? Well, here’s the science bit to prove it.

The Optimal Angle of Pull – (e)

The humble Christmas cracker consists of a reinforced barrel section (the bit in the middle) connected to the tail section at either end. (see below). When pulled, the cracker will always rip somewhere within the weak areas connecting the barrel to the tails, as indicated by the lines of likely failure on the diagram. If the tails are held in the same way and pulled straight backwards with an equal amount of force the cracker is equally likely to fail at either end – i.e. your chance of victory is just 50%. To improve your chances of winning the pull, you need to apply some scientific principles!

By pulling the cracker backwards and down at the same time it is possible to concentrate the force across the top face of the opponents line of likely failure making a failure at this point (indicated as "point of extra strain") more likely
A detailed mathematical analysis of the stresses involved has shown that the optimum downwards angle for pulling the cracker (e) is somewhere between 200 and 550, dependent on the geometry of the cracker and the material of manufacture

The equations describing the optimum angle of pull are complicated. Don’t event try to work it out unless you possess a degree in mathematics. Use ours instead!

How can I make sure that my calculations are correct?

To measure C, you need to take a piece of string and wrap it all the way around the circumference of the barrel. Make a mark, straighten it, and measure with a ruler. C & L can either be centimetres or inches, provided the same units are used for both.

Q is a factor relating to the quality of the cracker. It is found that the more expensive crackers tend to be constructed of superior quality, stronger material. As the quality of material improves the optimum angle of pull increases slightly. To determine factor Q, assess the quality of the cracker by visual examination. Q will have a value of 1, 2 or 3 as follows:

Q=1 Value or home made cracker where paper/foil is thin

Q=2 Standard cracker

Q=3 Luxury cracker constructed of sturdy materials

"It is usually possible to estimate the Q factor by just considering the price," continues Dr Bennett. "If you bought your crackers from Woolworths, then up Q by one point. Crackers from Woolies are better quality than their price would suggest."

Although the above equation only approximates the rigorous mathematical solution of optimal angle, the error is usually less than 50. This is a small error, especially when considering that, in practice, it is difficult to pull the cracker on exactly the calculated angle.

How am I sure that it really works?

For example, a standard cracker from Woolies has the following dimensions:

C = 18cm

L = 9cm

Generally, the quality factor Q would be assessed to be a 2. However being a Woolworths cracker, we will take Dr Bennett’s advice and increase the quality factor by one notch to 3. The desired angle of pull is calculated as follows:

e = (11 x 18/9) + (5 x 3) = 370

Getting It Just Right

In order to evenly spread the stress on your own side of the cracker whilst pulling the cracker back and downwards, it is crucial that the following actions be followed. It can take a little practice to master the technique.

The cracker should be gripped approximately one inch from the end of the tail closest to the barrel.

The thumb and forefinger should form a complete circle around the circumference of the tail. Do not stick the thumb out towards the barrel.

The tail should be kept in line with the barrel throughout the pull.

Twisting the tail during the pull should be avoided.

Pull the tail straight back and down without allowing any sideways movement.

Pull with an even steady force. Do not jerk the cracker.

Experimentation on a range of different crackers has demonstrated that, if all of the above principles are adopted, the chance of victory is increased from 50 to 73%.

Pulling the cracker back and upwards at the same calculated angle is equally effective. Although, this way, the prize inside the cracker will fall on the floor.