I was reading about the better volumetric efficiency of DOHC engines as compared to SOHC engine and was wondering if fuel efficiency is directly related to volumetric efficiency.
Volumetric efficiency though directly related to fuel efficiency on paper, it is not a deciding factor in the real world fuel efficiency of the vehicle.
There are other tons of parameters on the car which ultimately decide the fuel efficiency.
Still , People and engine builders prefer to have a engine with higher V.E because the relationship with V.E and Torque curve is much closer than that of V.E with fuel efficiency.
In Simple words higher V.E = slightly better torque curve rather than better Fuel efficiency.
That said even though the DOHC engine has about 95% V.E(which is sort of the limit for Naturally aspirated engine without tuning) has less torque at lower RPM and contradicts the above statement.
The reason for that is that in most DOHC layouts there is something called as variable valve timing which only opens the taps fully when in higher RPMs to improve economy at lower RPMs, so at higher RPMs you have better V.E in a DOHC engine.
This is one of the reasons why DOHC is better at higher RPMs than SOHC and that is its signature feature.