If I were to build a 16lb MTB over my 26lb Orange I would end up loosing 4.54 kg I would have lost ~4.5% of my total bike + me mass.
I am 94 KG kitted up.
That means my acceleraion is ~3.6% faster on flat smooth ground. Up hill on bumpy ground it is going to make some difference but not alot. The main difference will be on long climbs as you will tire a little less qucikly but not by much.
Lets say you do a climb at 7 mph and you have 100m height gain over 1000 m (I will assume the same tyres, pressures e.t.c) and you are me with at 95 Kg kitted up. Given the weight of the bike + me on either bike is nearly the same the rolling resistance will be nearly identical and I ignoring air resistance at these speeds. I am also ignoring the rotational K.E energy of the wheels as I want to do these sums today.
Light bike energy used in climb
= (101 x 9.81 x 100) +(0.5 x 101 x 3.1^2) ~ 99600 J
Ornage bike energy used
= (106 x9.81 x100) + (0.5 x 101 x 3.1^2) ~ 105000 J
Given the slope is 1000 m long and the speed is 7 mph or 3.1 m/s the time taken is 323 secs. Therefore the power output of me on the light bike is 308W 😯
On the heavier bike my power ouput is 325W. The difference is real and both figures would be higher if rolling resistance, air resistance and rotational K.E of the wheels is added in but the differences are not big either. Also I do not think I could sustain 308W.
Now doing more sums in my simplified model, if I was able to sustain 325W (I can’t) on the lighter bike I would save about 16 second at this power output on this fictious climb over being on the Orange. Which at my level of competitiveness is going to make sod all difference when I race but could affect placings for those after points.
P.S these numbers are fictious as I have ignored rolling resistance, air resistance and rotational K.E of the wheels. I have also assumed a flat hard climb at constant gradient and a rider who maintains a constant speed. When all these factors are taken into account I am sure the difference in time will be a fair bit less.
When I have tried light bikes I have felt a noticebale difference in the way it rides/ acclerates/ handles but I don’t think I was any faster in the real world.