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My 1978 R/100 stumbles on hard acceleration. After that the RPM rises at idle to about 2700. Where should I start.

Not enough information. Tell us more.

Here's some hints for what we need to know:
Did it JUST start doing this or did the condition sorta sneak-up on you?
Are you running stock ignition; points, "weights', etc or have you changed to some hybrid electronic system?
How old are your coils?
Have you EVER changed your Carburetor diaphragms?
Did you get the engine warm before setting the idle?
Are the "chokes" turning completely OFF, or has the choke cable pulled out of the little operator (where the lever is)?

"Please answer all questions and write your name and date at the top of your paper."

Hmm, nothing about capacitors in Jean's exam paper. You ok, Jean?

Test questions:
Hard to say if it started all of a sudden or gradually because this is part of an ongoing tuning effort.
I have the stock ignition, probably near 200K on the bike now. Off course points etc, have been changed often.
Coils with less than 6k and less than 3yrs. old.
Diaphrams were good last time I looked, about 40 miles ago.
Engine was warmed well before the idle started rising.
Chokes were off for sure.

Is the ignition advance unit all free and easy? springs? air leak? Do you have vacuum take off ports?

Use my simple test to diagnose if a high idle is due to the advance, or carbs.

Capacitor question is for next Friday's test.
Advanced topic.
Like Duane said...Advance?

In my experience, two things cause high idle after the engine is completely warmed up (20-25 mil ride). Most common is setting the idle when the engine is not fully warmed up. Second is having the idle set way too lean.

My 78 R100s used to stumble on acceleration...the main cure was new diaphragms, but I also put new coils on as I was running the original ones...I did this in 2005, I think. (Earlier I had installed new sp wires and NGK 5k plug capswith little improvement.) Another thing that caused poor acceleration was the inside of the main jet had deposits of gummy stuff way up inside where I could not see and it required complete main-jet disassembly to discover this.
Soaking in carb cleaner does not get this stuff out. The mid-range carb orifice might be clogged too.