if (sb.length() > 4000) {
    Log.v(TAG, "sb.length = " + sb.length());
    int chunkCount = sb.length() / 4000;     // integer division
    for (int i = 0; i <= chunkCount; i++) {
        int max = 4000 * (i + 1);
        if (max >= sb.length()) {
            Log.v(TAG, "chunk " + i + " of " + chunkCount + ":" + sb.substring(4000 * i));
        } else {
            Log.v(TAG, "chunk " + i + " of " + chunkCount + ":" + sb.substring(4000 * i, max));
        }
    }
}

// http://stackoverflow.com/questions/8888654/android-set-max-length-of-logcat-messages