VR and density
 

I'm currently reading Aircraft Performance, written by P.J. Swatton, and I got a bit confused regarding the rotation speed (VR) and how it is affected by density altitude. My understanding is that since VR is an indicated airspeed, an aircraft should lift off at the same indicated airspeed, with both low and high density.
However, in the book it is stated that if the density is decreased, VR will increase to produce enough lift required for lift off.

This statement will be true if we are talking about TAS, but is the same true for IAS?

Correct. However when the density is lower, the acceleration rate is slower (due less thrust) so VR can be delayed so that V2 is achieved by the time the aircraft reaches attitude "X" degrees pitch.

Never came across a performance calculation that applied density altitude to V spds. How would you? Applied to RTOW and allowed thrust, yes, but the speeds used were always those associated with calculated weight.

But wouldn't V1 vary with density since it will take longer to accelerate from V1 to VR with low density? And the same for V2, a lower density means that VMC is reduced and we can therefore have an reduced V2 (provided it still is above 1.13 VSR)?

Another small question; could someone tell me which (if any) airplane have a significant reduction in the single eng power-on stall speed?

Charts the start with an OAT and pressure altitude are essentially “ density altitude” charts, but no Part 25 perf data calls it density altitude, only Part 23.

VR largely is driven by the need to hit V2 at screen, having had a failure at the critical stage of the takeoff. So, anything which might affect V2 and rotation characteristics should have an effect on VR.

All the my charts for computing V speeds, including Vr have altitude and temperature parameters, and the computed speed is different with different altitudes and temperatures ... ergo Density Altitude is applied to the V speeds.

I admit my comment was not very clear as to my meaning. Terrible, now I read it. Indeed, the tables/i-pads are entered with altitude/QNH corrections and OAT. There will be latent calculations lurking in the backgrounds to take care of density. What I meant to say is that I had not seen a calculation where we had to make an adjustment to Vspds, directly, to account for density altitude. Of course it is inherent in the outcome of whatever method is used to calculate allowed weight & thrust & speeds.

Apologies for the confusion.