User blog:Dragonfriendsomega897/Tensa Zangetsu's Speed multiplier.

Bankai Byakuya compared to Shikai Ichigo.
Byakuya in his Bankai state can react to Ichigo in his Shikai state Byakuya's Senbon Zakura Kageyoshi is faster than Ichigo, as Ichigo is suprised how fast it is and how quicklyit could defend Byakuya and then appear behind him to strike him.

Therefore Bankai Byakuya's Speed => Shikai Ichigo's Speed.

Byakuya's Speed
A lieutenant can dodge and react to Negacion. Negacion is stated to be light and Hollow weak as Menos use it. A lieutenant reacting and deflecting Lille's attack. Lille's attack are light and they even reflect like light when it falls on a mirror. We know that Captain's are above Lieutenant's. We know Byakuya is a Captain.

Therefore Byakuya should atleast have Speed of Light Combat and Reaction speed. Byakuya has SOL combat speed (299,792,458 meters per second) and reaction speed which is 0.000000003336 seconds. Note - The combat speed and reaction speed don't matter to figure out the multiplier of Ichigo's Bankai.

Calc
After Ichigo transforms into his Bankai, the distance between Ichigo and Byakuya is 8.555... meters. According to Byakuya himself he lost sight of Ichigoand he couldn't even reaction.

Speed = Distance/Time. The Time here being the reaction speed of Byakuya which is the time it takes for him to react to something moving, Ichigo had to move to Byakuya before he could react so the Time should be below 0.000000003336 seconds. The Distance here is the distance between Ichigo and Byakuya and the distance Ichigo travelled which is 8.555... meters. ∴ Speed = 8.555.../0.000000003336. Bankai Ichigo's Speed = 2,564,891,029.555... m/s or 8.555 x SOL or 8.555... times faster than Bankai Byakuya.

If Bankai Ichigo is 8.555... times faster than Bankai Byakuya and Bankai Byakuya's speed is around Shikai Ichigo's Speed if not greater, then Ichigo's Bankai multiplies his Speed more than 8.555... times on top of his Shikai.

Conclusion - Ichigo's Bankai Speed multiplier = 8.555...+ x Speed of Shikai Ichigo.

Does this align with the series ?
As Yoruchi states in Chapter 120, the difference between Bankai and Shikai interms of combat ability is 5 to 10 times. Byakuya states, Tensa Zangetsu's ability is to fight at speed high speed. In Bleach: Official Character Book SOULs it states, "It (Tensa Zangetsu) channels all of the bankai power into speed, thus allowing the user (Ichigo) to battle at a feverish pace. "

So Tensa Zangetsu's combat ability is to increase speed, therefore the speed difference between Zangetsu and Tensa Zangetsu should be 5-10 times.

'''Conclusion - Ichigo's Bankai Speed multiplier is between 5-10 times or 8.555...+ x Speed of Shikai Ichigo to be precise and Ichigo in the Soul Society is 8.555... x The Speed of Light.'''