So we have BHP and we have Top speed. And we know that they are related. But how.
Now the point to note here is that, the top speed corresponds to that rpm beyond which the torque is just not sufficient to overcome the resistance factors. In other words, at that rpm the torque that reaches the backwheel exactly balances the frictional factors and there is nothing left to contribute to acceleration. So the acceleration stays zero and velocity is unchanging.
Now for a given bhp can we predict the top speed. Not easy as it needs to take into consideration a number of factors like gearing, weight, rolling resistance etc.
But there is a point about the torque curve that we can note; We know that after the max-torque rpm, the torque begins to drop, passing the max-bhp point soon.
Now obviously the topspeed-rpm has to lie beyond the max bhp rpm; Else the bike will never reach the max-bhp rpm while running.
Now to have maximum top speed, topspeed-rpm should lie as far away from the max-bhp rpm as possible; Now what does that mean - The torque curve should drop as slowly as possible. Now there is a restriction to this - If the torque curve drops very slowly, then very soon it will reach an rpm where the torque X rpm value is greater than the current max-bhp; Obviously this is not possible as there can be only one max-bhp point and we started off this analysis knowing its value.
So we can summarize as : for a given bhp, topspeed is maximum when the torque curve, on passing the max-bhp point, falls off as slowly as possible without posting a new max-bhp point.
Now lets try to come up with a crude formula for topspeed-bhp relation; Mind you, this is pretty crude, but as applicable to the sort of bikes that we see around here, it works fine.
The funamdamental information we would use here is that : The relation between power
and topspeed carries a factor of three; In other words, to increase the top speed
by a factor of one, you need to increase the power by a factor of three;
Mathematically, this appears as :
Power = (some constant) X (top speed)**3
for example, a bike puts out 15bhp and touches 115 kmphr - say. Now you want to increase the topspeed by 10% - ie, to 126.5 kmphr. For this the bhp would need to be increased by 30% - to 20bhp.
Now lets get down to how we can derive it.
As said earlier:
Power = (some constant) X (top speed)**3
ie, power = (some constant) X (top speed) X (top speed) X (top speed)
Now we need to find the value of this constant. For that we need the help of the old faithful - The Royal Enfield Bullet.
We know that the bullet has a power of around 18bhp and a top speed near 120kmphr. (sorry,but all speed readings im talkin abt in this are speedo readings...)
So the constant is : (lets call it K)
K = 18 / (33.33 X 33.33 X 33.33) = 0.0004861
(where 33.33 is the metre/second conversion of 120 kmphr)
So now we have a value of K.
Now the formula appears as :
Power = 0.0004861 X (Topspeed)**3
Lets try it one some known values. For shogun we know the power is 14bhp.So lets find the top speed :
just find the cube root of (14/0.0004861) .
Note that what you get is in meters/sec. On converting it into kmphr by multiplying with 18/5, It comes around to 110 kmphr. Pretty matches,right?
Now assume your RD goes to a top of 130 kmphr. Use the above formula to find the power.It comes to around 22.7bhp.
And if it goes to 140 , it comes around 28.6 .
And if it goes to 145, its more like 31 bhp!!
And for a value of 143 - its exactly 30.46....
Say for a samurai - if it goes to 90kmphr,the bhp calculation comes as 7.6 - same figures for a splendor,caliber etc..
Now say a 11 bhp bike,say RX 100 - formula gives the top speed as 103.68. So in the end we see that this seems to work for this range of bikes, where the different physical characteristics approximately come within the same class.
Note : This is just a crude formula that works kinda ok as far as these indian bikes are concerned. It overlooks a number of parameters, but in our context it gives reasonable resulsts.
In case you are interested, try out these C programs which implement this relation.