Monday, May 26, 2014

Mumbai - Rajasthan NRR situation over-analysed

Since posts related to the IPL seem to get me a lot of hits on this blog here is another one. Yesterday, while I was watching a rather boring Indy 500 race, I heard shouts and screams from our neighbors who are cricket fans. This quickly distracted me and thankful I was because I witnessed one of the most bizarre cricket match endings I have ever seen.

The confusion was huge, mathematical and needed some time to get round to. I believe that the teams, even after the scores were level at 14.3 overs had not a true idea of the situation. As this facebook post by Mayur suggests that even if 14.4 where a dot ball, the Mumbai Indians still had a shot at qualifying if they hit 14.5 for a boundary.

In fact, cricinfo has further gone ahead to explain that even if 14.4, 14.5 and 14.6 were a dot ball, Mumbai could still make it to the play off by hitting a six off the 15.1 delivery. Assuming of course sportsmanship from Rajasthan who would not ball a no-ball post 14.4.

Further analysis from an over the coffee table debate has spurred an interesting idea. I am going to argue that even if 15.1 were a dot ball - on paper, Mumbai still had a chance to make it to the play offs. All they had to do was a little rain dance.

No complication in cricket is complete without a discussion on the Duckworth Lewis system[citation needed]. In fact with all the confusion that was yesterday, I am surprised it was not mentioned.

Cricinfo's "net run rate explained" page tells us that -
"[if] a result is achieved under Duckworth/Lewis, for net run rate purposes Team 1 will be accredited with Team 2's Par Score on abandonment off the same number of overs faced by Team 2."
Which means that if it rained when the scores are level at 14.5 and the rest of the game abandoned, then Rajasthan's score would have been reduced. By how much? The D/L system calculation is clearly out of the scope of this blog post, But we do have this handy tool to help us.

These calculations suggest that Mumbai would have won by 58 runs if rain poured in at 14.5. Which would make the net run rate look like this -

Net Run Rate

This would qualify Mumbai for the play-offs and cause Twitter to accuse the Rain Gods to be Ambani's agents.

If no wicket falls this can go on till ball 16.4 where Rajasthan would be safe even from the rain Gods. Here is a plot for who would have won given ball when it rained, and Rajasthan did not concede an extra.

As the plot shows, Rajasthan could take 2 more wickets to seal the match earlier.

Friday, May 16, 2014

$2 Undecillion Lawsuit - An alternative solution

XKCD What-ifs are a pleasure to read. This week Lord Randall wrote about a $2 Undecillion Lawsuit. This what-if got me thinking in an alternative direction, and here is an alternative What-If to the same question.

If you have not read the XKCD article - in the $2 Undecillion Lawsuit a man called Anton Purisima has filed a lawsuit against Au Bon Pain Store, which if he wins will fetch him 2 Undecillion Dollars which is ($ 2 x 1036). Everything in the world can be purchased for $ 7.7 x 1012 so that is significantly more than all the money in the world.

As the xkcd article suggests, 2 undecillion dollars is comfortably higher by magnitudes to the sum total of the money that exists in the world. In modern times though, the sum total of money in the world is not such a clear concept. This is because day by day the world is becoming more of a credit based system than a cash based one. When you have a cash based system the sum total of money in the world is a finite. While things are more flexible when it comes to credit -

In case the Au Bon Pain Store did lose this lawsuit to Anton Purisima - in a cash based system Au Bon Pain simply could not pay. The best they can do is surrender all the cash that they have and everything that they own to Anton. Anton would be rich but not be the undecillionaire which he hopes to be with this lawsuit. However, in the credit based system there is still hope for Anton. All he has to do is convince a bank to loan 2 undecillion dollars to Au Bon Pain so that Au Bon Pain can pay him.

Why would a bank sanction such a sub-prime loan? For a bank to make such a loan, it must see a profit. The bank takes on risk when it gives out a loan and they like to bundle in the cost associated with this risk into the loan agreement via the interest rate or insurance. To offset the risk associated with a 2 undecillion dollar loan, there needs to be a massive payment as an incentive to make the loan. There is not enough money to make this payment but the bank knows that soon there will be one person who will be rich enough to pay. We are talking about Anton here. Anton is not going to be rich if the bank does not make a loan and the bank is not going to make a loan if Anton is not going to make the bank rich.

They strike a deal. Bank will make the loan to Au Bon Pain (with everything Au Bon Pain owns as mortgage), the court will send the money to Anton. In return, Anton must become a 'hyper-premiere' customer of the bank for which the bank will charge a modest one-time fee of 1.9 undecillion dollars. Anton will agree because it's better than nothing and still he will have more money than he can possibly spend.

This leaves 2 ridiculously rich entities in the world - the bank and Anton. They can buy anything and still have almost the same amount of money left over. Anton can do what he pleases with the money. The bank has an agenda though; it still has to make the other 0.1 undecillion dollars to balance its sheets. It made a loan against everything that Au Bon Pain has which is worthless compared to the loaned amount. It must raise the value of everything Au Bon Pain owns in that case, it has more than all the money in the world to do this.

If Au Bon Pain owned all its stores, then the bank can buy property around the stores at ridiculously high pricing driving the price of the property up. Not only has the price of the property gone up but the neighbours of the store are now suddenly ridiculously rich and Au Bon Pain can start charging astronomical prices because people don't know where to spend. This will not only happen to Au Bon Pain but to everything.

People will spend because everyone suddenly has a lot of money and the value of this money is falling fast. As more people have access to preposterous sums of money other people want some of it as well and prices will go up. Moreover, the government will be collecting huge taxes on all these transactions which means that the government will get spending and the inflation will spread like wild fire. The bank and Anton will have a gala time for a short while when they can buy anything they want. If they are fast enough, they can be the 'king / corporate entity of the world'. This will not really happen because people can refuse to sell but they can capture a significant portion of the world's stuff.

Something similar has actually happened before. This is the inflation chart of the Zimbabwean Dollar (If that looks steep then look again and find the logarithmic scale) -
When the Zimbabwean dollar was introduced, it was arbitrarily valued greater than the American Dollar, which was highly optimistic. The Zimbabwean economy was not in good shape and the exchange rate immediately went into freefall. People lost complete faith in the currency and dumped all the Zimbabwean dollars they had, making the fall worse. What eventually happened was that the country moved to using foreign currencies and cell phone talk-time as trading units.

So Anton and the bank will plunge the value of the American Dollar and the country will be forced to move to a foreign currency like the British Pound? Hold on. The banks would have thought of this, they will quickly realise that the USD will fall and will invest in a foreign currency. They will buy out all of it and take the foreign currency down with the dollar. This will go on until a new steady state is reached and the new crazy sum of money is significantly distributed. The world will temporarily move to barter before a new cash based (or limited credit) economy is set up.

The people who were opportunistic during this turmoil will become the new rich and the people who went on a tech detox vacation in the middle of a desert will be the new poor. There will be a complete redistribution reshuffling of the world's wealth. There is a good chance Anton and the bank will end up on the rich side of the new world. If you were a bank would you sanction this loan? I bet some bank would.

Side-note: The bank as per law will have to maintain minimum reserve, but it has to do that only at the end of the day. It can do this in two ways - act so fast that all the turmoil will happen in one day and they own enough barter at the end of it or they can also meet the minimum reserve with a deposit at the central bank, which can make the central bank panic and look for reserve.

Saturday, May 3, 2014

G-Train through the Center of the Earth

Humans have always looked up in the sky, fascinated more by birds than moles, we built hot air balloons, the Wright brothers flew and finally NASA took us to the moon (Which is almost 5 decades ago, but that is a rant for another blog post). Humans have travelled 384,400 kms to the moon and the voyager is away from the Earth. What we have not done is scratched the Earth’s surface.

An old QI episode (G for Gravity) talked about drilling a hole through the center of the Earth and the travel time if the tunnel was frictionless through it would be 42 minutes and 12 second. This is called a “Gravity Train” and is quite a popular concept. The more interesting thing about the “Gravity train” is that it does not need to pass through the center of the Earth. Even if we cut a cord across any point of the Earth to another, the train will get from one end to the other in ~42 minutes in frictionless conditions.

A gravity train route that cuts through a chord of Earth looks like this –

If we move things around such that Gravity always points down then the gravity train looks like a massive roller coaster –

This seems to be a great solution to the world transportation problem. Get from anywhere to anywhere in less than 43 minutes and the only energy that is required be used to overcome friction and drag. You start at the top of the roller coaster, build momentum, go as far as you can up the other way and top up with some power when steam runs out due to friction.

However, it is difficult to drill a hole through the center of the Earth. It is surprising how quickly we will get to magma if we start digging downwards, after about 20-30kms of digging and you have almost created a man-made volcano! (More on this evil plan in a future blog post) Meanwhile, we will dig sideways. The furthest we have gotten in terms of drilling deep is the Al Shaheen Oil Field  ~12.5kms which is a surprising 0.19% of the distance to the center of the Earth, and this was a bore hole and not quite a tunnel. Suppose we could tunnel this deep – How far can our gravity train travel?

So from the plot above if we can dig a tunnel that has a max depth of 12.5 kms which is close to the deepest drilled hole we have today we can travel ~810 kms on the surface of the Earth. That is Bangalore – Mumbai, New York – Detroit and London – Zurich in less than an hour. That is an average speed of ~1000km/hr. What’s more, there is heavy return for development of technology, for every 1 km we can go deeper, we can travel ~ 30 kms more on the ground in the same time.

All we need is some focused energy to get this done. Half a century ago people thought going to the moon was a ludicrous idea. It’s difficult to convince investors why it is worthwhile to go to the moon today, but we can convince them that this will change the world and be profitable. It’s been almost 50 years since we were on the moon, come on engineers – Challenge Accepted?

Friday, May 2, 2014

Shank Lengths of Bolts

Bolts and nuts are the most crucial part of any assembly. They hold the different components of the vehicle together by providing the structural strength required. Selection and the usage of bolts, nuts and other fasteners are a very critical aspect of engineering design and should be considered with high importance at the design phase of the vehicle.

A very common mistake on Formula Student and Baja cars that is seen is the incorrect selection of bolts in terms of their sizes and shank lengths. Before proceeding here is the clarification of the shank length and threaded length -
Bolts are designed to carry axial loads. It may carry bending loads as well however it is important to understand which areas of the bolt should see the bending load. To get a better idea of why this is - consider a rod that needs to be broken. A force is applied in bending because it is the weakest then (Why? -  Load PathsDesign Error Blog).
If the rod still does not snap the next best thing to do is create a notch like in the picture below. It should be easier to break this after that. The notch can be really tiny, but it has an associated stress concentration factor which will cause it to see higher stress in that region and break faster. The notch is also a perfect crack initiation point for the rod to break.

The threads on the bolts are nothing but a series of notches when the bolt comes under bending and the bolt is much likely to break when loaded in bending at the threaded region. 
The threaded length of the bolt is the section which should be used to fasten the nut onto the bolt and for that reason only, all the other bending load must be taken up by the shank region. Which means that a bolt that connects a rod-end to the chassis mounts must look like this -

The clamps and the spacers and the rod end see the shanked length of the bolt and the threaded length of the bolt only starts under the final washer after which the nut is tightened and torqued up. At least 2 threads should be visible on the other end of the nut to ensure that the bolt is properly fastened.
This not only applies to the suspension bolts but any critical bolt that might be used in the vehicle. This mistake is also often seen in brake balance bars there bolts or even studs are used and the brake forces travel right through the threaded region of the bolt / stud. That will break. Custom engine mounts often ignore this as well and we see these bolts bend and break with time.

This blog post is originally written for the Formula Student India website and has been cross posted from here.