Category Archives: Engineering

Financial side of Akashi-Kaiko bridge

Akashi-Kaiko bridge is world’s longest suspension bridge (total length= 4km; suspended length=2km ). It is located in Japan connecting two main islands called Honsu and Sikoku. Recently I had chance to visit this bridge. Yes, as a civil engineer I can say this bridge is awesome, magnificent and beautiful. During construction, this bridge suffered a big earthquake that increased its span by about 0.80m than original length.  Thanks to Japanese high tech and safety measures, only 6 injury occurred to build this bridge and no one lost life during 10 years of construction works.

Besides its technical marvels, i was also interested in hidden parts – financial and economical side of this bridge.

Wikipedia mentions – “The total cost is estimated at 500 billion yen, and is expected to be repaid by charging drivers a toll to cross the bridge. The toll is 2,300 yen and the bridge is used by approximately 23,000 cars per day. At 2300 yen/car annual revenue would equal 19.5 billion yen. Given the interest expense on 500 billion yen, this bridge will never be repaid. But annual revenue is around 4% of investment, so with near zero interest rates in Japan, the bridge will pay for itself in 30 years, plus enable the growth of the overall economy in the region.”

I had doubt on the wiki’s statement. So, I did some research with authentic publications. After some study i found that, wiki is partially correct.

The bridge was build during the times when roads and trains were under Japanese government control. 67% of the investment for the construction of this bridge (and the related highway) was done by central government and rest were divided between 10 other local governments. Interestingly, all the government investments were at 0% interest rate.

In addition, loans were taken in the form of government guaranteed bond, private sector bond and pure loans. Similarly, Japan Railway also had small investment (although there is no train way in Akashi-Kaiko bridge, there is train ways in other bridge connecting two islands which same company operates, hence the loan).

How the investment will be paid back?
In 1990s, there was change in government policies and many government bodies were privatized. This resulted in complicated system of revenue collection and payment system for the bridge. Railway has to pay to the Highway company for leasing the train ways. In addition, the highway itself collects the toll. The total revenue is to be split up for loan payback and maintenance and operation of bridge.

Figure below shows the summary of payment method.

As wiki mentioned earlier, the cost of bridge is so huge that even with cumulative traffic tolls, the revenue will not be sufficient to payback  the normal interest rate. However, as most of the investment was done by government at 0% interest rate, the pay back period of this bridge is estimated to be about 45 years (including cost of highways).

The fact remains that investment by government in such massive projects becomes mandatory if we want to develop the society as a whole.

Just side note: Government of Japan has taken massive loans from World Bank for infrastructure development. However, most of the loans were re-payed in 1990s and now there is almost no loans left to be repaid.



Japanese grammer notes

In this post i will try to simplify the essence of Japanese grammar rules. The verbs and adjectives are the core of Japanese grammar. These verbs and adjectives take different forms depending upon time(past, present,future), conjugation and level of respect shown.

An attempt will be made in this post to show all the rules in single place so that it can be grasped easily.

1. Japanese Language has basically three forms of verbs

Group I verb In this group, the last sound of the ます form is that of い line e.g. かきます; のみます
Group II verb In this group, the last sound of the ます form is that of え line e.g.たべます; みせます; みます*
Group III verb Verb of this group ends at します and noun denoting action +します e.g.

2. Japanese Language has basically two types of adjectives (い & な)

3. Verb has different forms viz. plane form, dictionary form, ない form, masu form etc

4. Rules to change to Te(て) form for verbs

Group I verb Depending upon the sound, the て form varies as follows e.g. かきます; のみます
Group II verb Replace ます with て e.g.たべます; みせます; みます*
Group III verb Replace ます with て e.g.

5. Present continuous tense (V-ing) form is represented as Vーて  います

To memorize some Japanese words go here.

Multiple linear regression analysis with constraints

Here is how to do it:
Suppose the linear model is of the form y=b1x1+b2x2+b3x3,

subject to b1+b2+b3=1.

We have to do is simply re-express b3 as b3=1−b1−b2,
which is to say you are trying to build a model of the form

So create new variables y`=y-x3, x1`=x1−x3, and x2`=x2−x3, and perform the normal linear regression using these transformed variables as the independent variables.

Note that: In excel there is build in function called ‘solver’ which appears that it can be used by maximizing R^2 value and setting the constraints b1+b2+b3=1, but this wont work. The solver is good for solving ‘linear programming’ and not regression type of questions.

Radius of earth (classical trignometry)

Question: Suppose that, while lying on a beach near the equator watching the sun set over a calm ocean, you start a stopwatch just as the top of the sun disappears. You then stand, elevating your eyes by a height H=1.7m, and stop the watch when the top of the sun again disappears. If the elapsed time is t=11.1 secs, what is the radius r of the earth?

One day=24hrs=86400sec

The earht rotate 2*pi() in one day=2*pi=6.2832 radians

angle traversed in 11.1sec=0.000807215 radians

observation height=1.7m


Download calculation file

A thought on remaining happy

being happy is easy. Trying to know why we are happy leads us to vicious circle. We will find one reason that will explain why we are happy. But the question arises again why that reason makes us happy and so on.