Rough idle and slow take off at any light. Hardly any horse power

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Car idle is rough Inspection Service & Cost A rough idling engine can be caused by a number of issues, some of them are serious while others tend to be minor, but the symptoms remain pretty much the same. The car will feel rough and bouncy when the engine is running. The car will also idle below its regular speed, display inconsistent RPMs and may produce a shaking, skipping or slipping sound when the vehicle is running.
While a rough idling engine may seem to be a simple inconvenience it often indicates a deeper problem within the engine. The vehicle should be inspected and repaired as soon as possible because small problems have a way of turning into expensive repairs. How this system works: The idle speed of an engine is basically the rotational speed the engine runs on when it is un-coupled from the drivetrain and the throttle pedal is not being depressed. The idle speed is measured in the revolutions per minute of the crankshaft.
When an engine is running at idle speed it generates enough power to smoothly operate equipment such as the water pump, alternator, and power steering but not enough power to move the vehicle itself. A passenger car will usually idle between 600 RPMs and 1000 RPMs. A properly functioning idle should run smoothly without skipping or slipping. Common reasons for this to happen:

• Dirty Fuel Injectors: The fuel injection system injects fuel into the cylinders, which creates a mix of air, and fuel to ignite and burn. Fuel injectors have tiny nozzles to spray the fuel into the cylinder and they can become clogged over time. clogged or failing fuel injector creates a lack of fuel in the vehicle's engine. This can cause a rough idle, it can also cause symptoms such as slow acceleration or the car not feeling as if it has enough power. If the problem is addressed early, it is possible to clean the injectors, which will restore them to full function. If this condition is not addressed in a timely manner the injectors will need to be replaced. Incorrect Idle Speed: While the average idle speed falls between 600 to 1,000 RPMs, if your vehicle is experiencing a rough idle it could be due to an incorrect idle speed setting. A trained mechanic can easily adjust the idle speed, and it should stay at the proper speed. If an adjusted idle speed becomes inconsistent or changes at random intervals there may be a bigger problem that needs to be explored. Vacuum Leak: If the vacuum system has a leak, it can seriously affect the ability of the vehicle's computer to regulate the air to fuel ratio. This can lead to a rough idle and if the problem is not addressed the car may experience slow acceleration and a lack of power. Vacuum leaks should be inspected and repaired immediately. Incorrectly Installed or Damaged Plugs: Spark plugs are responsible for creating the spark that allows the vehicle to burn fuel. If spark plugs are improperly installed or malfunctioning, the idle speed can be affected. The vehicle's engine may vibrate or there may be slipping or straining sounds coming from the engine. Defective or Clogged Fuel Pump: A rough idle can be related to fuel delivery issues. The fuel pump, which is responsible for pulling fuel from the gas tank to the fuel injectors, can become clogged or defective. If this happens the engine will not get enough fuel, which can cause a rough idle, sputtering, stalling and even slow acceleration. Clogged Fuel Filter: A clogged fuel filter can cause similar problems. The job of the fuel filter is to screen out contaminants in the fuel, over time it will become clogged and need to be replaced. A rough idle is one symptom of a clogged fuel filter. Failing Electrical Components: A problem or failure in the ignition system or various electronic components can cause a rough idle. If this is the case, the problem will usually get worse as RPMs increase. Common culprits include the ignition control module, plug wires, coils, and spark plugs. Defective Airflow Sensor: A defective airflow sensor can be responsible for a rough idle. A mass airflow sensor detects the amount of air coming into the fuel injection system and sends that information to the vehicle's computer. The computer uses that data to deliver the proper amount of fuel to the air in the vehicle. Over time these sensors can malfunction or become dirty. One of the first symptoms of a malfunctioning airflow sensor is a rough idle. The car may also accelerate slowly and even stutter or stall as the problem progresses. Dirty Oxygen Sensor: Oxygen sensors measure how rich or lean the gases are as they exit the combustion chamber. Depending on the results, the amount of fuel entering the engine is adjusted by the vehicle computer. The ultimate goal is to maintain an ideal mixture that produces the lowest emissions. A dirty or failing oxygen sensor will usually trigger the check engine light and can lead to a rough idle, lower fuel efficiency and failed emission test.

Sounds like you have a cylinder(s) that is not firing. Newer cars have a separate igniter (high voltage ignition coil) for each plug - check them all and I am sure you will find a culprit to replace.

If the battery light only comes on when the idle gets rough (and usually that means slow like it wants to stall), that is not unusual. If the engine starts stumbling and running very slow, the alternator will not be able to produce the power necessary to completely power the car. Then the battery is tasked with picking up the slack during those periods. When that happens, the battery light will come on. If the battery is on all the time, then you need to have the charging system tested.

The ac compressor pulls a good number of horses from a 4 cyl engine.
Any minor performance problem is amplified when the ac is running.
You probably have a weak spark plug or wire, or an issue with an injector.
Is the check engine light coming on when it is rough ?

It is hardly ever the spark plug or only the spark plug - generally for some reason there is a weak or lost spark and the reason must be found and rectified by carefully checking and then replacing any components found to be edfective - plug wires, coil, distributor cap, rotor (if fitted), wiring, connections and could conceivably even be the ECU. Perhaps the misfire is due to injector trouble...

Sometimes a fault with persist even after it has been "cured" until the fault code is erased with diagnostic equipment.

Possible Idle air control, simple to change on the throttle body

Do you know if the plugs were changed, a bad or broken plug will also cause rough idle and slow acceleration?

Check all the old hoses or vacuum lines leading to the manifold...i found a small crack in one of my lines that was causing me a rough idle..of course it was way in the back were i could hardly see it...use an inspection mirror and take your time. also a plugged cooling sensor lie leading to the throttle body could possibly cause this problem too..it senses the temperature and regulates the idle circuitry.

Sounds like a possible vaccume hose leak?