B-1: Fill & Download for Free

Years ago someone was kicking around the idea of turning the B-1 into an interceptor. The aircraft would be called the B-1RThe idea was simple give the B-1 an air to air radar and load up the bomb bays and any outboard pylons with AMRAAMs. The problem with all big fighters is they are expensive. Boeing decided to turn the F-15 into a missile truck with over 20 missiles with the F-15X.

Most people look at the B-1B and the Tu-160 and think “Hey look, the Russians copied another one of our bombers!” And you know what? I understand the misconception. I mean, look at them!Here is what you don't get looking at these pictures though… one of these planes is much larger, much heavier, and has much more powerful engines than the other.The Tu-160 is 26% heavier, with 2.2x the wing area and 81% more thrust than the B-1B!The two aircraft could hardly be considered in the same class at all if not for their payloads. The B-1 can carry about 25% more weapons.So why such different aircraft even though they look so similar? Mostly they were designed with different missions. See, the Tu-160 was NOT Russia’s answer to the B-1B.The B-1 was never envisioned to be as large or as fast as the Tu-160. But Russia never believed that, until we actually put them into service. No, they had another aircraft in mind when sizing the Tu-160.Enter the B-70, or more accurately the XB-70.This aircraft was larger and faster than the Tu-160. It is in fact, to the Tu-16o as the Tu-160 is to the B-1B. Nearly out of its class.See, the B-70 was cancelled. It was expensive, complicated, and had performance that was in many ways considered ‘disruptive’. The ultimate irony here is one of the reasons it was cancelled was it was thought to be too provocative a weapon system to have. There was concern that fielding such a bomber would force the Soviets to attempt to match it. Ironic because when it was cancelled many in Russia DIDN'T BELIEVE IT! They were instead convinced that the project went dark and we continued it in secret. And when it never materialized and the B-1 program kicked off, they then again thought this was the B-70 returned and that the size and performance numbers for the B-1 were all disinformation.But, Russia could not match the B-70, so they aimed for a target between a B-1 (which they thought was a fake cover) and the B-70 (which they thought was what we were really building).So much for not provoking Russia, huh?Then the B-1 was cancelled, because the B-2 was coming online. And when the B-1 program was restarted (campaign promise of the Reagan administration) its mission changed from high altitude supersonic penetration to low altitude supersonic penetration. So its top speed was slashed and it made compromises for signature and low altitude supersonic performance.The Tu-160 is a beautiful aircraft in my opinion. So is the B-1. If we made an up-scaled version of the B-1, I'm sure we could match the speed and high altitude performance of the Tu-160, but we didn't and so the world has two very similar looking, but very different and yet very capable aircraft.

1+2+3+4+5…..= -1/12Yeah! The fact that the sum of natural numbers till infinity is equal to -1/12 completely blew me.It's weird and nonsensical to even think that the sum of positive integers till infinity can give a definite value, that too a negative fraction.Google ImageWell, this equation was given by Ramanujan and is known as The Ramanujan Summation. Let's look over the proof now.Let, A = 1-1+1-1+1-1….The summation of the above series can be 0 or 1, depending upon the number of terms it has, even or odd respectively.Now subtracting A from 1 we get,1-A = 1-(1-1+1-1+1….)1-A = 1-1+1-1….Eventually, the Right Hand Side equals A.So, 1-A = AOr A =1/2Now let's take another series—B= 1-2+3-4+5-6……Therefore,A-B = (1-1)+(2-1)+(-3+1)+(4-1)….A-B = 1-2+3–4+5–6…. = BA=2BB= 1/4Now coming to our main interest, let—C = 1+2+3+4+5….C-B = (1-1) + {2-(-2)} + (3-3) + {4-(-4)}….C-B = 4+8+12….C-B = 4(1+2+3+4…..)C-B = 4(C)3C = -BC = -1/12Amazing! Isn't it?But we know this isn't true. The sum of infinite positive integral series must be an infinity. Hence, the result makes no sense.Then where are we wrong?We were wrong at assuming the value of 1+2+3….=C. By doing this, we had already assumed it's value to be a well defined where all the algebraic calculations could be done. But this is untrue. How can we assume it's value to be a real quantity when it is infinite?But this equation has it's use in String Theory and is still a debatable equation of all time!SS_Sources:-The Ramanujan Summation: 1 + 2 + 3 + ⋯ + ∞ = -1/12?Is sum of Natural Numbers upto Infinity -1/12??Ramanujan summation - Wikipedia