Some morning maths: Calculating Head Speed with 15-20% Headroom for Governor Control

[RcRotaryMadness]

Morning all,

I've been doing a little maths on a power setup for an E550 FBL - If you could cast your eyes over it and give me your opinion I'd appreciate it... also might be helpful to newbie’s..

Motor - 6S 1220 KV
Main Gear - 111 T

Desired head speeds: 1,850 for Hovering and 2,000 for idle up (for Aerobatic flight not full 3D)

I think a LiPo of 6S rather than 5S as higher voltage = lower current

And I'd like 15% Headroom for hovering left at the end of the flight (3.7v)

And I'd like 20% Headroom for flying (4.2v)


So some maths...


4.2v Per cell X 6S = 25.2V
25.2V x 1220KV = 30,744 motor rpm
30,744 x 0.90 (10% loss due to motor efficiency etc) = 27,669 Motor Rpm


Now 111T main gear divided into a pinion of 10T (111/10) = a 11.1 Gear Ratio
Or a 111T main gear divided into a pinion of 11T (111/11) = a 10.1 Gear Ratio

SO

27,669 Motor rpm / 11.1 = 2,492 (This would be max calculated head speed at zero pitch, full throttle)

Now to calculate the Governors Headroom, Formula: (capable head speed – Desired Head speed)/Capable Head speed = % Headroom
2,492-1850/2492 = 25% Headroom @ 1,850 HS (Take off)
2,492-2000/2492 = 19% Headroom @ 2,000 HS (Idle Up)


These are at Take off with a fully charged lipo



Now for 3.7V (end of flight voltage)

3.7v Per cell X 6S = 22.2V
22.2V x 1220KV = 27,084 motor rpm
27,084 x 0.90 (10% loss due to motor efficiency etc) = 24,375 Motor Rpm


Now 111T main gear divided into a pinion of 10T (111/10) = a 11.1 Gear Ratio
Or a 111T main gear divided into a pinion of 11T (111/11) = a 10.1 Gear Ratio

SO

24,375 Motor rpm / 11.1 = 2,195 (This would be max calculated head speed at zero pitch, full throttle)

Now to calculate the Governors Headroom:

2,195 -1850/2,195 = 15% Headroom @ 1,850 HS (landing)
2,195 -2000/2,195 = 8% Headroom @ 2,000 HS (Idle Up)

So everything’s ok apart from the 8% headroom for idle up as the battery starts to drain... So lets run the figures again but with an 11T pinion:





25.2V on a 111T main gear divided into a pinion of 11T (111/11) = a 10.1 Gear Ratio

SO

27,669 Motor rpm / 10.1 = 2,739 (This would be max calculated head speed at zero pitch, full throttle)

Now to calculate the Governors Headroom, Formula: (capable head speed – Desired Head speed)/Capable Head speed = % Headroom
2,739 -1850/2,739 = 32% Headroom @ 1,850 HS (Take off)
2,739 -2000/2,739 = 27% Headroom @ 2,000 HS (Idle Up)


At 22.2V (end of flight):

24,375 Motor rpm / 10.1 = 2,413 (This would be max calculated head speed at zero pitch, full throttle)

Now to calculate the Governors Headroom, Formula: (capable head speed – Desired Head speed)/Capable Head speed = % Headroom
2,413 -1850/2,413 = 23% Headroom @ 1,850 HS (Take off)
2,413 -2000/2,413 = 17% Headroom @ 2,000 HS (Idle Up)


So here we would have better headroom and so less bogging BUT as its a larger pinion and larger headrooms, i’d expect flight time to be less and the motor/esc run hotter


So its take your pick I guess. Whats your opinion?

Cheers
Matt

[Mark_T]

I think I would have used - MrMel headspeed calculator v3

Not all ESC Governors are created equal and it is handy to be able to take that into account.

Nice run through the maths though.

[RcRotaryMadness]

Going off Mr Mels calc a 10T pinion would do the job... So my maths ties in with his calc...

I have used these calcs BUT i do like to run through the maths myself so I know where all the numbers are coming from... from the start of the flight to the end...

I think i'm gonna go with a 10T pinion to start and go for a 11T pinion if it starts bogging too early on in the flight..

I just want get it hovering to start with tho..

BTW this would be using a Vbar as the governor not an ESC's built in one..

Cheers

[jimmyhorns]

After all that, so glad I still run nitro

[RcRotaryMadness]

lol... the thought of nitro simplicity did cross my mind while doing the above... but then memories of oily muck and noisey engines reminded me why I went electric

[jimmyhorns]

The smell and muck of nitro reassures my wife im not having an affair

[panosg]

The smell and muck of nitro reassures my wife im not having an affair

Har har I smell of oil and petrol every day...... I am a mechanic My wife knows I have an affair with engines!