Worried about the long, steep hill on my commute

A lot of people like 1.95-2.25" semi-slicks. I took a pinch flat from gravel and the wider tires are more reliable b/c they absorb shocks better.
 
As an engineer I attempt to solve problems based on science,I run the numbers.I hope you can follow me: we'll deal with the hill first.I work in the MKS system (universal except for the US, thanks to that Reagan nitwit);your weight+ bike I will guess generously at 115 kg (250 lbs),the incline is 800ft over 3 miles or 5280 ft,that means a 5.1% grade. The force required to get you+bike up that hill is: 0.051*115= 5.9 kg (13 lbs ,* means multiply).Now we will figure out how much power it takes to get you up that hill at a certain speed,say 20 mph.(32 km/h),32km/h is 32000/3600=8.9 m/sec (29 ft/sec).
The power required is: Force times speed or:
5.9*8.9=53 kgm/sec .But that does not take the wind & rolling resistance into account. Guess at around 0.5 HP,one HP=75 kgm/sec., 0.4 HP =30 kgm/sec .Total power reqd is 30+53=83 kgm/sec or 1.1 HP.Assuming 85% drivetrain efficiency we need 1.3HP to get up that hill at 20 mph,and correspondingly less at other speeds,for instance at 15mph it would take about 3/4*1.3=1HP and it would take you 12min to get up that hill,instead of 9 min at 20mph
You have the choice of a fixed gear ratio (much cheaper) or the variable speed NuVinci hub + Staton gearbox ,(expensive but flexible, also heavy). In the fixed ratio we have the Staton gearbox and the GeBe kevlar belt drive or the DAX Titan countershaft setup. As far as engines go, forget the Chinese (HT) engines,too unreliable.Reasonable choices are the 49cc Honda or DAX Titan.Both engines have a power capability of around 2.5HP but should,in my opinion not be run at over 1.5HP continuously.
With fixed drive you have a basic problem,to get up the long hill you need to gear down sufficiently to have enough torque, where the rubber meets the road,but you would prefer not to overrev the engine either when cruising on the flats.Peak torque for these engines occurs at around 5k rpm,at around 80% of max power or 2HP,derating this by 30 % to have something to spare we can count on having 1.4 HP on hand at 5krpm.That's enough.
There is a basic relationship between power (P) torque (T) and speed N (rpm),P= 0.0002*N*T , at 5000 rpm with 1.4 ft lbs torque the power delivered is :0.0002*5000* 1.4 =1.4HP which is more than the 1.3 we needed at 20 mph.With a 26" wheel, 20 mph corresponds to 270 rpm,so we need reduction of 5000/270=18.5
This is all well and good, but how will we be doing on the flats?.If we limit the rpm to 6.5 k we get a speed of 26mph and you could at 7.5k rpm you can get up to 30mph (bad idea)
How to get the 18.5 reduction?.The Staton gearbox has a 18.75 reduction so, a 1:1 from the gearbox to the rearwheel would do nicely.They have a hub with a freewheel input from the engine.The DAX Titan has a built in 5.0 reduction and a 1:1 to the jack shaft so you need around a 3.7 reduction.10t to 36t rear sprocket would be about right.There is no freewheel in this drive train, only the centrifugal clutch.One thing to bear in mind is that such a clutch does not disengage if you throttle back unless you brake to a sufficiently low speed.So you could use engine braking going down hill.With a freewheel you have to rely totally on your brakes,watch out for overheating.I guess you are going to find the DAX setup a lot cheaper than the Staton.I am a bit leery of the DAX engines,will the Titan last ???.Fuel consumption is not much different between engines,it takes a certain amount of energy to get up that hill and your fuel has to supply it. I hope you were able to follow my design process,good luck
 
As an engineer...

... I hope you were able to follow my design process,good luck

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This is probably the slowest (speed) bench racing anyone's ever done... ;)
 
Tortoise & the hare,while you all,HT speed freaks are racing along,**** the torpedos to your next breakdown (you should pull along a trailer with tools+spare engine),we plodding engineers pass you by,could lend a hand,or first aid as required.
I understand you now have two of these Chinese jewels,smart move,you might keep at least one running at the time.Makes things exciting if you're a glutton for random punishment.Have fun and be sure to carry plenty of life insurance.Someone might appreciate that.
 
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