There has been some talk in rec.sport.snowmobiles about Titanium Jack or
Drive shafts. These items are sold with the catch phrase of "reduces
rotating mass." While this is true, it isn't really the rotating mass that
matters. What really matters is the "rotational Inertia."
Rotational inertia is to rotation what mass is to linear acceleration.
Rotational inertia takes into account how far the rotating mass is from the axis
of rotation. Solid round bars have very little rotational inertia because the
mass is very close to the axis of rotation.
Below is a table that tells how much energy (hp) is required to rotationally
accelerate a steel jackshaft vs. a titanium jackshaft at various vehicle speeds.
W is the rotational velocity of the jackshaft in radians per
second. Alpha is the rotational acceleration of the jackshaft
in radians per second squared. The rotational inertia is in
kg-m^2. The values for the rotational velocity and acceleration were derived
from the data from the 1995 Shoot Out at the Old Forge as reported by American
Snowmobiler for the Vmax 600 (I know the gear ratios etc for this sled). This
assumes no track slip and average acceleration between points was used. I also
made the same calculations for a Steel vs. an Aluminum light weight brake rotor.
Note that accelerating the brake rotor requires about 35 times more
power than accelerating the jackshaft.
I also calculated the power that would be required to accelerate the brake
rotor if it were mounted to the drive shaft. Since the drive shaft spins slower
than the jackshaft the power required is less. To the best of my knowledge none
of the manufacturers have ever tired to mount the brake rotor to the drive shaft
(I know there would be some complications in doing this). (ed. note: there is an
aftermarket mountain sled manufacturer working on just such a modification,
details to follow soon!)
The power required to accelerate a mass in a straight line is equal to:
P=mass*acceleration*velocity. I also calculated the power required to linearly
accelerate the shafts. It is interesting that more power is required to
accelerate the shafts linearly than rotationally. Since the linear acceleration
dominates in this case, you could drop 2 lb. much more cost effectively than by
using a titanium shaft and you would get about the same advantage. A steel
jackshaft weighs about 6 lb and a titanium shaft would weigh about 3.6 lb.
Northern Lights (406) 892-0240 sells an aluminum composite brake rotor that
is 66% lighter than steel. It is probably cheaper than a titanium jackshaft and
would yield much better benefits.
Steel vs. Titanium Jackshaft Rotational Drive
Set Inertia W Alpha hp Shaft hp
60 ft
Ti 0.000141 437.2 238.16 0.0197 0.0058
St 0.000233 0.0325 0.0095
330 ft
Ti 0.000141 619.4 65.3 0.0076 0.0022
St 0.000233 0.0126 0.0037
1/8th mile (660 ft)
Ti 0.000141 691.97 22.9 0.0030 0.0009
St 0.000233 0.0050 0.0014
1/4 Mile (1320 ft)
Ti 0.000141 790.65 17.68 0.0026 0.0008
St 0.000233 0.0044 0.0013 Steel vs Aluminum Composite Brake Rotor hp for Rotor
Set I W Alpha hp mounted to
Drive Shaft
60 ft
Al 0.0027956 437.2 238.16 0.3904 0.1141
St 0.008314 1.1609 0.3392
330 ft
Al 0.0027956 619.4 65.3 0.1516 0.0443
St 0.008314 0.4510 0.1318
1/8th Mile (660 ft)
Al 0.0027956 691.97 22.9 0.0594 0.0174
St 0.008314 0.1767 0.0516
1/4 Mile (1320 ft)
Al 0.0027956 790.65 17.68 0.0524 0.0153
St 0.008314 0.1559 0.0455 Steel vs. Titanium Shaft - Power for Linear Acceleration
Set Mass V Acc hp
60 ft
Ti 1.711 21.67 11.8 0.5867
St 2.83 0.9704
330 ft
Ti 1.711 30.7 3.24 0.2282
St 2.83 0.3775
1/8 mile (660 ft)
Ti 1.711 34.3 1.14 0.0897
St 2.83 0.1484
1/4 Mile (1320 ft)
Ti 1.711 39.2 0.875 0.0787
St 2.83 0.1302 | 
