put power back on the catenary to power other trains). Economics In 1991 (the final year of the Soviet Union) the cost of electrifying one kilometre was 340–470,000 roubles and required up to 10 tonnes of copper. Thus it was expensive to electrify. Are the savings due to electrification worth the cost? As compared to inefficient steam locomotives, it's easy to make the case for electrification. But how does electrification economically compare with diesels locomotives which started to be introduced in the USSR in the mid 1930s and were significantly less costly than steam traction? Later on there were even whole books written on the topic of comparing the economies of electric vs. diesel traction Electrification requires high fixed costs but results in savings in operating cost per tonne-km hauled. The more tonne-km, the greater this savings, so that higher traffic will result in savings that more than cover the fixed costs. Steep grades also favor electrification, partly because regenerative braking can recover some energy when descending the grade. Using the formula below to compare diesel to electric on a double track line with Ruling gradient of 0.9 to 1.1% and density of about 20 million t-km/km (or higher) results in less cost for electric with an assumed 10% return required on the capital investment. For lower traffic, diesel traction will be more economical per this methodology. Return on investment formula The decision to electrify is supposed to be based on return on investment and examples are given which proposed electrification only if the investment in electrification would not only pay for itself in lower operating cost but in addition would give a percentage return on the investment. Example percentage returns on investment are 10% and 8%. In comparing two (or more) alternatives (such as electrification or dieselization of a rail line) one calculates the total annual cost, using a certain interest return on capital and then selects the least cost alternative. The formula for total annual cost is: Эпрi=Эi+ЕнКi where the subscript i is the i th alternative (all the other letters except i are in the Russian alphabet), Эi is the annual cost of alternative i (including amortization of capital), Ен is the interest rate, and Кi is the value (price) of the capital investment for alternative i. But none of the references cited here (and elsewhere) call Ен an interest rate. Instead, they describe it as the